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Journal articles on the topic 'Adams-Bashforth'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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1

Murni, Delvitri, Bukti Ginting, and Narwen . "PENERAPAN METODE ADAMS-BASHFORTH-MOULTON ORDE EMPAT UNTUK MENENTUKAN SOLUSI PERSAMAAN DIFERENSIAL LINIER HOMOGEN ORDE TIGA KOEFISIEN KONSTAN." Jurnal Matematika UNAND 5, no. 2 (May 23, 2016): 21. http://dx.doi.org/10.25077/jmu.5.2.21-25.2016.

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Abstrak. Persamaan diferensial linier homogen orde tiga koesien konstan direduksimenjadi persamaan diferensial biasa orde-1, yaitu y0= f(x; y) dengan syarat awaly(x0) = y. Persamaan diferensial biasa orde-1 diselesaikan menggunakan metodeRunge-Kutta orde empat untuk menentukan nilai pendekatan y01; y2; dan y. Selanjutnya,digunakan metode Adams-Bashforth orde empat untuk menentukan nilai pendekatany; ; dst sebagai prediktor. Nilai yang ditampilkan oleh metode Adams-Bashforthorde empat digunakan pada metode Adams-Moulton orde empat sebagai korektor. Prosesmetode Adams-Bashforth orde empat dan metode Adams-Moulton orde empat dikatakansebagai metode Adams-Bashforth-Moulton orde empat atau metode prediktor-korektor.

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2

Misirli, Emine, and Yusuf Gurefe. "Multiplicative Adams Bashforth–Moulton methods." Numerical Algorithms 57, no. 4 (November 23, 2010): 425–39. http://dx.doi.org/10.1007/s11075-010-9437-2.

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3

Ewald, Brian. "Weak Versions of Stochastic Adams-Bashforth and Semi-implicit Leapfrog Schemes for SDEs." Computational Methods in Applied Mathematics 12, no. 1 (2012): 23–31. http://dx.doi.org/10.2478/cmam-2012-0002.

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AbstractWe consider the weak analogues of certain strong stochastic numerical schemes, namely an Adams-Bashforth scheme and a semi-implicit leapfrog scheme. We show that the weak version of the Adams-Bashforth scheme converges weakly with order 2, and the weak version of the semi-implicit leapfrog scheme converges weakly with order 1. We also note that the weak schemes are computationally simpler and easier to implement than the corresponding strong schemes, resulting in savings in both programming and computational effort.

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4

Ma, Shichang, Yufeng Xu, and Wei Yue. "Numerical Solutions of a Variable-Order Fractional Financial System." Journal of Applied Mathematics 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/417942.

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The numerical solution of a variable-order fractional financial system is calculated by using the Adams-Bashforth-Moulton method. The derivative is defined in the Caputo variable-order fractional sense. Numerical examples show that the Adams-Bashforth-Moulton method can be applied to solve such variable-order fractional differential equations simply and effectively. The convergent order of the method is also estimated numerically. Moreover, the stable equilibrium point, quasiperiodic trajectory, and chaotic attractor are found in the variable-order fractional financial system with proper order functions.

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5

Hahm, Nahm-Woo, and Bum-Il Hong. "A GENERALIZATION OF THE ADAMS-BASHFORTH METHOD." Honam Mathematical Journal 32, no. 3 (September 25, 2010): 481–91. http://dx.doi.org/10.5831/hmj.2010.32.3.481.

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6

Kar, Sajal K. "An Explicit Time-Difference Scheme with an Adams–Bashforth Predictor and a Trapezoidal Corrector." Monthly Weather Review 140, no. 1 (January 1, 2012): 307–22. http://dx.doi.org/10.1175/mwr-d-10-05066.1.

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Abstract A new predictor-corrector time-difference scheme that employs a second-order Adams–Bashforth scheme for the predictor and a trapezoidal scheme for the corrector is introduced. The von Neumann stability properties of the proposed Adams–Bashforth trapezoidal scheme are determined for the oscillation and friction equations. Effectiveness of the scheme is demonstrated through a number of time integrations using finite-difference numerical models of varying complexities in one and two spatial dimensions. The proposed scheme has useful implications for the fully implicit schemes currently employed in some semi-Lagrangian models of the atmosphere.

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7

Peinado, J., J. Ibáñez, E. Arias, and V. Hernández. "Adams–Bashforth and Adams–Moulton methods for solving differential Riccati equations." Computers & Mathematics with Applications 60, no. 11 (December 2010): 3032–45. http://dx.doi.org/10.1016/j.camwa.2010.10.002.

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8

Segarra, Jaime. "MÉTODOS NUMÉRICOS RUNGE-KUTTA Y ADAMS BASHFORTH-MOULTON EN MATHEMATICA." Revista Ingeniería, Matemáticas y Ciencias de la Información 7, no. 14 (July 15, 2020): 13–32. http://dx.doi.org/10.21017/rimci.2020.v7.n14.a81.

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n este estudio, el objetivo principal es realizar el análisis de los métodos numéricos Runge-Kutta y Adams Bashforth-Moulton. Para cumplir con el objetivo se utilizó el sistema de ecuaciones diferenciales del modelo Lotka-Volterra y se usó el software matemático Wolfram Mathematica. En los resultados se realiza la comparación de los métodos RK4, AB4 y AM4 con el comando NDSolve utilizando el modelo Lotka-Volterra. Los resultados obtenidos en los diagramas de fase y la tabla de puntos de la iteración indicaron que el método RK4 tiene mayor precisión que los métodos AB4 y AM4.

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9

JANKOWSKA, MAŁGORZATA, and ANDRZEJ MARCINIAK. "ON EXPLICIT INTERVAL METHODS OF ADAMS-BASHFORTH TYPE." Computational Methods in Science and Technology 8, no. 2 (2002): 46–57. http://dx.doi.org/10.12921/cmst.2002.08.02.46-57.

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10

Kumar, Sunil, Ali Ahmadian, Ranbir Kumar, Devendra Kumar, Jagdev Singh, Dumitru Baleanu, and Mehdi Salimi. "An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets." Mathematics 8, no. 4 (April 10, 2020): 558. http://dx.doi.org/10.3390/math8040558.

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In this paper, the operational matrix based on Bernstein wavelets is presented for solving fractional SIR model with unknown parameters. The SIR model is a system of differential equations that arises in medical science to study epidemiology and medical care for the injured. Operational matrices merged with the collocation method are used to convert fractional-order problems into algebraic equations. The Adams–Bashforth–Moulton predictor correcter scheme is also discussed for solving the same. We have compared the solutions with the Adams–Bashforth predictor correcter scheme for the accuracy and applicability of the Bernstein wavelet method. The convergence analysis of the Bernstein wavelet has been also discussed for the validity of the method.

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11

Atangana, Abdon, and Kolade M. Owolabi. "New numerical approach for fractional differential equations." Mathematical Modelling of Natural Phenomena 13, no. 1 (2018): 3. http://dx.doi.org/10.1051/mmnp/2018010.

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In the present case, we propose the correct version of the fractional Adams-Bashforth methods which take into account the nonlinearity of the kernels including the power law for the Riemann-Liouville type, the exponential decay law for the Caputo-Fabrizio case and the Mittag-Leffler law for the Atangana-Baleanu scenario.The Adams-Bashforth method for fractional differentiation suggested and are commonly use in the literature nowadays is not mathematically correct and the method was derived without taking into account the nonlinearity of the power law kernel. Unlike the proposed version found in the literature, our approximation, in all the cases, we are able to recover the standard case whenever the fractional powerα= 1. Numerical results are finally given to justify the effectiveness of the proposed schemes.

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12

Liao, Hongyun, Yipeng Ding, and Ling Wang. "Adomian Decomposition Algorithm for Studying Incommensurate Fractional-Order Memristor-Based Chua’s System." International Journal of Bifurcation and Chaos 28, no. 11 (October 2018): 1850134. http://dx.doi.org/10.1142/s0218127418501341.

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Based on the definitions of fractional-order differential and Adomian decomposition algorithm, the numerical approximate solution of the incommensurate fractional-order memristor-based Chua’s system is investigated. Dynamical characteristics of the proposed system are studied by using phase diagram, bifurcation analysis and power spectrum. Research results show that compared with the Adams–Bashforth–Moulton algorithm, the Adomian decomposition algorithm yields more accurate results and its solution generally converges more rapidly. Compared with 3.776 achieved by the Adams–Bashforth–Moulton algorithm, the minimum order of the incommensurate fractional-order memristor-based Chua’s system solved by using Adomian decomposition algorithm is 1.76, which is much smaller. A reliable and efficient binary test for chaos, called “0–1 test”, is utilized to detect the presence of chaotic attractors in the system dynamics.

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13

Tutueva, Aleksandra, Timur Karimov, and Denis Butusov. "Semi-Implicit and Semi-Explicit Adams-Bashforth-Moulton Methods." Mathematics 8, no. 5 (May 13, 2020): 780. http://dx.doi.org/10.3390/math8050780.

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Multistep integration methods are widespread in the simulation of high-dimensional dynamical systems due to their low computational costs. However, the stability of these methods decreases with the increase of the accuracy order, so there is a known room for improvement. One of the possible ways to increase stability is implicit integration, but it consequently leads to sufficient growth in computational costs. Recently, the development of semi-implicit techniques achieved great success in the construction of highly efficient single-step ordinary differential equations (ODE) solvers. Thus, the development of multistep semi-implicit integration methods is of interest. In this paper, we propose the simple solution to increase the numerical efficiency of Adams-Bashforth-Moulton predictor-corrector methods using semi-implicit integration. We present a general description of the proposed methods and explicitly show the superiority of ODE solvers based on semi-implicit predictor-corrector methods over their explicit and implicit counterparts. To validate this, performance plots are given for simulation of the van der Pol oscillator and the Rossler chaotic system with fixed and variable stepsize. The obtained results can be applied in the development of advanced simulation software.

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14

Omolehin, J. O., M. A. Ibiejugba, M. O. Alabi, and D. J. Evans. "A New Class Of Adams-Bashforth Schemes For Odes." International Journal of Computer Mathematics 80, no. 5 (May 2003): 629–38. http://dx.doi.org/10.1080/0020716021000023051.

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15

Al-Sulami, Hamed, Moustafa El-Shahed, Juan J. Nieto, and Wafa Shammakh. "On Fractional Order Dengue Epidemic Model." Mathematical Problems in Engineering 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/456537.

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This paper deals with the fractional order dengue epidemic model. The stability of disease-free and positive fixed points is studied. Adams-Bashforth-Moulton algorithm has been used to solve and simulate the system of differential equations.

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16

Lang, Nguyen Duc, Tran Gia Lich, and Le Duc. "Two approximation methods of spatial derivatives on unstructured triangular meshes and their application in computing two dimensional flows." Vietnam Journal of Mechanics 28, no. 4 (December 31, 2006): 230–40. http://dx.doi.org/10.15625/0866-7136/28/4/5584.

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Two approximation methods (the Green's theorem technique and the directional derivative technique) of spatial derivatives have been proposed for finite differences on unstructured triangular meshes. Both methods have the first order accuracy. A semi-implicit time matching methods beside the third order Adams-Bashforth method are used in integrating the water shallow equations written in both non-conservative and conservative forms. To remove spurious waves, a smooth procedure has been used. The model is tested on rectangular grids triangulari2jed after the 8-neighbours strategy. In the context of the semi-implicit time matching methods, the directional Derivative technique is more accurate than Green's theorem technique. The results from the third order Adams-Bashforth scheme are the most accurate, especially for discontinuous problems. In this case, there is a minor difference between two approximation techniques of spatial derivatives.

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17

Danca, Marius-F., and Nikolay Kuznetsov. "Matlab Code for Lyapunov Exponents of Fractional-Order Systems." International Journal of Bifurcation and Chaos 28, no. 05 (May 2018): 1850067. http://dx.doi.org/10.1142/s0218127418500670.

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In this paper, the Benettin–Wolf algorithm to determine all Lyapunov exponents for a class of fractional-order systems modeled by Caputo’s derivative and the corresponding Matlab code are presented. First, it is proved that the considered class of fractional-order systems admits the necessary variational system necessary to find the Lyapunov exponents. The underlying numerical method to solve the extended system of fractional order, composed of the initial value problem and the variational system, is the predictor-corrector Adams–Bashforth–Moulton for fractional differential equations. The Matlab program prints and plots the Lyapunov exponents as function of time. Also, the programs to obtain Lyapunov exponents as function of the bifurcation parameter and as function of the fractional order are described. The Matlab program for Lyapunov exponents is developed from an existing Matlab program for Lyapunov exponents of integer order. To decrease the computing time, a fast Matlab program which implements the Adams–Bashforth–Moulton method, is utilized. Four representative examples are considered.

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18

Feng, Xinlong, Tao Tang, and Jiang Yang. "Stabilized Crank-Nicolson/Adams-Bashforth Schemes for Phase Field Models." East Asian Journal on Applied Mathematics 3, no. 1 (February 2013): 59–80. http://dx.doi.org/10.4208/eajam.200113.220213a.

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AbstractIn this paper, stabilized Crank-Nicolson/Adams-Bashforth schemes are presented for the Allen-Cahn and Cahn-Hilliard equations. It is shown that the proposed time discretization schemes are either unconditionally energy stable, or conditionally energy stable under some reasonable stability conditions. Optimal error estimates for the semi-discrete schemes and fully-discrete schemes will be derived. Numerical experiments are carried out to demonstrate the theoretical results.

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19

Suescun-Díaz, Daniel, Diego A. Rasero-Causil, and Jaime H. Lozano-Parada. "Neutron Density Calculation Using the Generalised Adams-Bashforth-Moulton Method." Universitas Scientiarum 24, no. 3 (November 20, 2019): 543–63. http://dx.doi.org/10.11144/javeriana.sc24-3.ndcu.

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This paper presents a numerical solution to the equations of point kinetics for nuclear power reactors, a set of seven coupled differential equations that describe the temporal variation of neutron density and the concentration of delayed neutron precursors. Due to the nature of the system, we propose to numerically solve the point kinetics equations by implementing the Adams-Bashforth and Adams-Moulton methods, which are predictor-corrector schemes with their respective modifiers to increase precision. The proposed method was tested computationally for different forms of reactivity with up to six groups of delayed neutron precursors. This method was used in a recent publication to solve the inverse problem of finding the reactivity. In this work, it is shown that it can also be used for the calculation of nuclear power, that it is simple and easy to implement, and that it produces good results when compared with those in the literature for neutron population density and concentration of delayed neutron precursors.

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20

Kuzairi, Kuzairi, Tony Yulianto, and Lilik Safitri. "APLIKASI METODE ADAMS BASHFORTH-MOULTON (ABM) PADA MODEL PENYAKIT KANKER." Jurnal Matematika "MANTIK" 2, no. 1 (October 30, 2016): 14. http://dx.doi.org/10.15642/mantik.2016.2.1.14-21.

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Cancer is a deadly disease that is characterized by the growth of abnormal cells, the growth is ongoing, forming a tumor. Tumors are divided into two parts, namely benign and malignant tumors. Malignant tumors are a general term for cancer. The disease of cancer has a mathematical model in the form of a system of differential equations, for it required a method to obtain the solution of the system of differential equations. The method used is the method of numerical methods Bashforth Adams Moulton (ABM) order one, two, three, and four. From the results of this study concluded that the method ABM order three better than the method ABM first order, second order and fourth order at issue models of cancer, It can be seen in the graphic simulation using ABM order three, it shows that increasing time population of immune effector cells (E) and a population of effector molecules (C) increased and then stabilized. The population of immune effector cells (E) stabilized at 33.3336, while the population of the effector molecule (C) is stable in the scope of the numbers 33,333, 33,333 are said to be in scope for changes in population effector molecule (C) can not be known with certainty. While the population of cancer cells (T) remains at 0 at each iteration (stable) remains in a state that is free of cancer

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21

Marciniak, Andrzej, and Malgorzata A. Jankowska. "Interval methods of Adams-Bashforth type with variable step sizes." Numerical Algorithms 84, no. 2 (July 29, 2019): 651–78. http://dx.doi.org/10.1007/s11075-019-00774-y.

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22

Golmankhaneh, Alireza K., Roohiyeh Arefi, and Dumitru Baleanu. "The Proposed Modified Liu System with Fractional Order." Advances in Mathematical Physics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/186037.

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The chaos in a new system with order 3 is studied. We have shown that this chaotic system again will be chaotic when the order of system is less than 3. Generalized Adams-Bashforth algorithm has been used for investigating in stability of fixed points and existence of chaos.

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23

Rosu, Florin. "Parallel Algorithm for Numerical Methods Applied to Fractional-order System." Scalable Computing: Practice and Experience 21, no. 4 (December 20, 2020): 701–7. http://dx.doi.org/10.12694/scpe.v21i4.1837.

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A parallel algorithm is presented that approximates a solution for fractional-order systems. The algorithm isimplemented in CUDA, using the specific GPU capabilities. The numerical methods used are Adams-Bashforth-Moulton (ABM) predictor-corrector scheme and Diethelm’s numerical method. A comparison is done between these numerical methods that adapts the same algorithm for the approximation of the solution.

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24

MAZZONE, A. M. "VERLET METHODS WITH STEPSIZE CONTROL FOR MOLECULAR DYNAMICS CALCULATIONS." International Journal of Modern Physics C 12, no. 01 (January 2001): 31–38. http://dx.doi.org/10.1142/s0129183101001377.

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This study presents a stepsize control method for the numerical integration of ordinary differential equations. The method is based on the difference between a Verlet coordinates evaluation and an Adams–Bashforth coordinates predictor and can be easily implemented in existing Molecular Dynamics simulations. Numerical tests are made on the equilibrium configuration of crystalline silicon at low temperature.

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25

Shabana, Ahmed A., Dayu Zhang, and Gengxiang Wang. "TLISMNI/Adams algorithm for the solution of the differential/algebraic equations of constrained dynamical systems." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 232, no. 1 (July 31, 2017): 129–49. http://dx.doi.org/10.1177/1464419317718658.

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This paper examines the performance of the 3rd and 4th order implicit Adams methods in the framework of the two-loop implicit sparse matrix numerical integration method in solving the differential/algebraic equations of heavily constrained dynamical systems. The variable-step size two-loop implicit sparse matrix numerical integration/Adams method proposed in this investigation avoids numerical force differentiation, ensures satisfying the nonlinear algebraic constraint equations at the position, velocity, and acceleration levels, and allows using sparse matrix techniques for efficiently solving the dynamical equations. The iterative outer loop of the two-loop implicit sparse matrix numerical integration/Adams method is aimed at achieving the convergence of the implicit integration formulae used to solve the independent differential equations of motion, while the inner loop is used to ensure the convergence of the iterative procedure used to satisfy the algebraic constraint equations. To solve the independent differential equations, two different implicit Adams integration formulae are examined in this investigation; a 3rd order implicit Adams-Moulton formula with a 2nd order explicit predictor Adams Bashforth formula, and a 4th order implicit Adams-Moulton formula with a 3rd order explicit predictor Adams Bashforth formula. A standard Newton–Raphson algorithm is used to satisfy the nonlinear algebraic constraint equations at the position level. The constraint equations at the velocity and acceleration levels are linear, and therefore, there is no need for an iterative procedure to solve for the dependent velocities and accelerations. The algorithm used for the error check and step-size change is described. The performance of the two-loop implicit sparse matrix numerical integration/Adams algorithm developed in this investigation is evaluated by comparison with the explicit predictor-corrector Adams method which has a variable-order and variable-step size. Simple and heavily constrained dynamical systems are used to evaluate the accuracy, robustness, damping characteristics, and effect of the outer-loop iterations of the proposed implicit schemes. The results obtained in this investigation show that the two-loop implicit sparse matrix numerical integration methods proposed in this study can be more efficient for stiff systems because of their ability to damp out high-frequency oscillations. Explicit integration methods, on the other hand, can be more efficient in the case of non-stiff systems.

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26

Coudière, Yves, Charlie Douanla-Lontsi, and Charles Pierre. "Exponential Adams–Bashforth integrators for stiff ODEs, application to cardiac electrophysiology." Mathematics and Computers in Simulation 153 (November 2018): 15–34. http://dx.doi.org/10.1016/j.matcom.2018.04.006.

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27

Tavakkol, Sasan, Sangyoung Son, and Patrick Lynett. "Adaptive third order Adams-Bashforth time integration for extended Boussinesq equations." Computer Physics Communications 265 (August 2021): 108006. http://dx.doi.org/10.1016/j.cpc.2021.108006.

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28

Awati, Vishwanath B., Krishna B. Chavaraddi, and Priya M. Gouder. "Effect of boundary roughness on nonlinear saturation of Rayleigh-Taylor instability in couple-stress fluid." Nonlinear Engineering 8, no. 1 (January 28, 2019): 39–45. http://dx.doi.org/10.1515/nleng-2018-0031.

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Abstract The boundary roughness effects on nonlinear saturation of Rayleigh-Taylor instability (RTI) in couple-stress fluid have been studied using numerical technique on the basis of stability of interface between two fluids of the system. The resulting fourth order ordinary nonlinear differential equation is solved using Adams-Bashforth predictor and Adams-Moulton corrector techniques numerically. The various surface roughness effects and surface tension effects on nonlinear saturation of RTI of two superposed couple-stress fluid and fluid saturated porous media are well investigated. At the interface, the surface tension acts and finally stability of the problem is discussed in detail.

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29

Puelz, Charles, and Béatrice Rivière. "A priori error estimates of Adams-Bashforth discontinuous Galerkin Methods for scalar nonlinear conservation laws." Journal of Numerical Mathematics 26, no. 3 (September 25, 2018): 151–72. http://dx.doi.org/10.1515/jnma-2017-0011.

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Abstract In this paper we show theoretical convergence of a second-order Adams-Bashforth discontinuous Galerkin method for approximating smooth solutions to scalar nonlinear conservation laws with E-fluxes. A priori error estimates are also derived for a first-order forward Euler discontinuous Galerkin method. Rates are optimal in time and suboptimal in space; they are valid under a CFL condition.

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Sene, Ndolane, Babacar Sène, Seydou Nourou Ndiaye, and Awa Traoré. "Novel Approaches for Getting the Solution of the Fractional Black–Scholes Equation Described by Mittag-Leffler Fractional Derivative." Discrete Dynamics in Nature and Society 2020 (July 25, 2020): 1–11. http://dx.doi.org/10.1155/2020/8047347.

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The value of an option plays an important role in finance. In this paper, we use the Black–Scholes equation, which is described by the nonsingular fractional-order derivative, to determine the value of an option. We propose both a numerical scheme and an analytical solution. Recent studies in fractional calculus have included new fractional derivatives with exponential kernels and Mittag-Leffler kernels. These derivatives have been found to be applicable in many real-world problems. As fractional derivatives without nonsingular kernels, we use a Caputo–Fabrizio fractional derivative and a Mittag-Leffler fractional derivative. Furthermore, we use the Adams–Bashforth numerical scheme and fractional integration to obtain the numerical scheme and the analytical solution, and we provide graphical representations to illustrate these methods. The graphical representations prove that the Adams–Bashforth approach is helpful in getting the approximate solution for the fractional Black–Scholes equation. Finally, we investigate the volatility of the proposed model and discuss the use of the model in finance. We mainly notice in our results that the fractional-order derivative plays a regulator role in the diffusion process of the Black–Scholes equation.

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Tian, Ying Liang, Shu Guang Guo, and De Long Wu. "The Study on Measurement Method of Glass Melts' Surface Tension at High Temperature." Advanced Materials Research 889-890 (February 2014): 732–36. http://dx.doi.org/10.4028/www.scientific.net/amr.889-890.732.

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At high temperature conditions, the glass molten by the combined action of gravity and surface tension form an oval. Through digital image measurement system we can obtain glass molten oval contours and the contact angle. By the Bashforth-Adams equation which deduced from Young- Laplace equation to obtain the glass molten' surface tension at the corresponding temperature conditions. This method has good reproducibility and accuracy.

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32

Koca, Ilknur, and Pelin Yaprakdal. "A new approach for nuclear family model with fractional order Caputo derivative." Applied Mathematics and Nonlinear Sciences 5, no. 1 (March 31, 2020): 393–404. http://dx.doi.org/10.2478/amns.2020.1.00037.

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AbstractA work on a mathematical modeling is very popular in applied sciences. Nowadays many mathematical models have been considered and new methods have been used for approaching of these models. In this paper we are considering mathematical modeling of nuclear family model with fractional order Caputo derivative. Also the existence and uniqueness results and numerical scheme are given with Adams-Bashforth scheme via fractional order Caputo derivative.

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33

Arianti, Liatri, Rusli Hidayat, and Kosala Dwija Purnomo. "PENYELESAIAN MODIFIKASI MODEL PREDATOR PREY LESLIE-GOWER DENGAN SEBAGIAN PREY TERINFEKSI MENGGUNAKAN ADAMS BASHFORTH MOULTON ORDE EMPAT." Majalah Ilmiah Matematika dan Statistika 19, no. 2 (September 2, 2019): 53. http://dx.doi.org/10.19184/mims.v19i2.17268.

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Eco-epidemiology is a science that studies the spread of infectious diseases in a population in an ecosystem where two or more species interact like a predator prey. In this paper discusses about how to solve modification Leslie Gower of predator prey models (with Holling II response function) with some prey infected using fourth order Adams Bashforth Moulton method. This paper used a simple disease-spreading model that is Susceptible-Infected (SI). The model is divided into three populations: the sound prey (which is susceptible), the infected prey and predator population. Keywords: Adams Basforth Moulton, Eco-epidemiology Holling Tipe II, Local stability, Leslie-Gower, Predator-Prey model

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Riyadi, Mohamad, and Daswa Daswa. "SOLUSI HAMPIRAN PERSAMAAN LOGISTIK NON-AUTONOMOUS." Jurnal Edukasi dan Sains Matematika (JES-MAT) 5, no. 1 (April 21, 2019): 63. http://dx.doi.org/10.25134/jes-mat.v5i1.1745.

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The aim of this study is to derive the approximation solution of the non-autonomous logistic equation with a non-constant carrying capacity. The solution is found via predictor-corrector method (Adams-Bashforth-Moulton method, Milne method and Hamming method). The approximation solution that obtained, then, is compared to the exact solution. The results show that, for small step size, the approximation solution approximate the exact solution is in good agreement.

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35

Yépez-Martínez, H., and J. F. Gómez-Aguilar. "Numerical and analytical solutions of nonlinear differential equations involving fractional operators with power and Mittag-Leffler kernel." Mathematical Modelling of Natural Phenomena 13, no. 1 (2018): 13. http://dx.doi.org/10.1051/mmnp/2018002.

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Analytical and numerical simulations of nonlinear fractional differential equations are obtained with the application of the homotopy perturbation transform method and the fractional Adams-Bashforth-Moulton method. Fractional derivatives with non singular Mittag-Leffler function in Liouville-Caputo sense and the fractional derivative of Liouville-Caputo type are considered. Some examples have been presented in order to compare the results obtained, classical behaviors are recovered when the derivative order is 1.

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Rchid Sidi Ammi, Moulay, Mostafa Tahiri, and Delfim F. M. Torres. "Local existence and uniqueness for a fractional SIRS model with Mittag–Leffler law." General Letters in Mathematics 10, no. 2 (June 2021): 61–71. http://dx.doi.org/10.31559/glm2021.10.2.7.

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In this paper, we study an epidemic model with Atangana-Baleanu-Caputo fractional derivative. We obtain a special solution using an iterative scheme via Laplace transformation. Uniqueness and existence of a solution using the Banach fixed point theorem are studied. A detailed analysis of the stability of the special solution is presented. Finally, our generalized model in the derivative sense is solved numerically by the Adams-Bashforth-Moulton method.

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Jeng, Siow W., and Adem Kilicman. "Fractional Riccati Equation and Its Applications to Rough Heston Model Using Numerical Methods." Symmetry 12, no. 6 (June 5, 2020): 959. http://dx.doi.org/10.3390/sym12060959.

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Rough volatility models are recently popularized by the need of a consistent model for the observed empirical volatility in the financial market. In this case, it has been shown that the empirical volatility in the financial market is extremely consistent with the rough volatility. Currently, fractional Riccati equation as a part of computation for the characteristic function of rough Heston model is not known in explicit form and therefore, we must rely on numerical methods to obtain a solution. In this paper, we will be giving a short introduction to option pricing theory (Black–Scholes model, classical Heston model and its characteristic function), an overview of the current advancements on the rough Heston model and numerical methods (fractional Adams–Bashforth–Moulton method and multipoint Padé approximation method) for solving the fractional Riccati equation. In addition, we will investigate on the performance of multipoint Padé approximation method for the small u values in D α h ( u − i / 2 , x ) as it plays a huge role in the computation for the option prices. We further confirm that the solution generated by multipoint Padé (3,3) method for the fractional Riccati equation is incredibly consistent with the solution generated by fractional Adams–Bashforth–Moulton method.

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Suescún-Díaz, D., D. A. Rasero Causil, and J. H. Figueroa-Jimenez. "Adams-Bashforth-Moulton method with Savitzky-Golay filter to reduce reactivity fluctuations." Kerntechnik 82, no. 6 (December 18, 2017): 674–77. http://dx.doi.org/10.3139/124.110842.

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Masjed‐Jamei, Mohammad, Zahra Moalemi, Hari M. Srivastava, and Iván Area. "Some modified Adams‐Bashforth methods based upon the weighted Hermite quadrature rules." Mathematical Methods in the Applied Sciences 43, no. 3 (December 5, 2019): 1380–98. http://dx.doi.org/10.1002/mma.5954.

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Çelik, Vedat. "Bifurcation Analysis of Fractional Order Single Cell with Delay." International Journal of Bifurcation and Chaos 25, no. 02 (February 2015): 1550020. http://dx.doi.org/10.1142/s0218127415500200.

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This paper presents the bifurcation analysis of fractional order model of delayed single cell which is proposed for delayed cellular neural networks with respect to the time delay τ. The bifurcation points, time delay τc, are determined by modified Mikhailov stability criterion for a range of fractional delayed cell order 0.3 ≤ q < 1. Numerical results obtained from Adams–Bashforth–Moulton method demonstrate that the supercritical Hopf bifurcation occurs in the system.

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Bitimanova, Saltanat Serikbaevna, and Asel Asylbekovna Abdildaeva. "Algorithm for optimal control of electric power systems." Bulletin of Toraighyrov University. Energetics series, no. 4.2020 (December 17, 2020): 78–91. http://dx.doi.org/10.48081/wddo6475.

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This paper provides information about the current state of the energy system in Kazakhstan. Also, analyzing the technical condition of the structure of the Kazakhstan electro power station, a mathematical model for complex power systems is developed. Algorithms of control with Adams-Bashforth multistep method are developed. There has been conducted the analysis and assessment of significant factors affecting the forecasted dynamics of electric power consumption, built based on multivariate regression and cointegration models.

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Liu, Yadong, and Wenjun Liu. "Chaotic behavior analysis and control of a toxin producing phytoplankton and zooplankton system based on linear feedback." Filomat 32, no. 11 (2018): 3779–89. http://dx.doi.org/10.2298/fil1811779l.

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In this paper, we study the dynamic behavior and control of the fractional-order nutrientphytoplankton-zooplankton system. First, we analyze the stability of the fractional-order nutrient-plankton system and get the critical stable value of fractional orders. Then, by applying the linear feedback control and Routh-Hurwitz criterion, we yield the sufficient conditions to stabilize the system to its equilibrium points. Finally, Under a modified fractional-order Adams-Bashforth-Monlton algorithm, we simulate the results respectively.

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Chiou, J. C., and S. D. Wu. "On the generation of higher order numerical integration methods using lower order Adams–Bashforth and Adams–Moulton methods." Journal of Computational and Applied Mathematics 108, no. 1-2 (August 1999): 19–29. http://dx.doi.org/10.1016/s0377-0427(99)00096-5.

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Marin, Regina Paiva Melo, and Paulo Marcelo Tasinaffo. "Uma metodologia de modelagem empírica utilizando o integrador neural de múltiplos passos do tipo Adams-Bashforth." Sba: Controle & Automação Sociedade Brasileira de Automatica 21, no. 5 (October 2010): 487–509. http://dx.doi.org/10.1590/s0103-17592010000500005.

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Este artigo apresenta e desenvolve uma metodologia empírica alternativa para modelar e obter as funções de derivadas instantâneas para sistemas dinâmicos não-lineares através de um treinamento supervisionado utilizando integradores numéricos neurais de múltiplos passos do tipo Adams-Bashforth. Esta abordagem a rede neural desempenha o papel das funções de derivadas instantâneas que é acoplada à estrutura do integrador numérico, que efetivamente, é o responsável em realizar as propagações no tempo apenas através de uma combinação linear de redes neurais feedforward com respostas atrasadas. É um fato importante que somente os integradores numéricos de mais alta ordem aprendem efetivamente as funções de derivadas instantâneas com precisão adequada, o que comprova o fato de que os de primeira ordem somente conseguem aprender as derivadas médias. Esta abordagem é uma alternativa à metodologia que trata os problemas de modelagem neural em estruturas de integração de passo simples do tipo Runge-Kutta de alta-ordem, sendo esta, mais robusta e complexa na determinação da retropropagação, que exige - neste caso - o emprego da regra da cadeia para funções compostas. Ao final deste artigo são apresentadas simulações de resultados numéricos dos integradores neurais de Adams-Bashforth em três estudos de caso: 1) pêndulo não-linear sem variáveis de controle; 2) um modelo abstrato com controle e 3) sistema de Van der Pol.

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McHugh, J. P., and D. Barkey. "Nonlinear evolution of a thin anodic film." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2202 (June 2017): 20160930. http://dx.doi.org/10.1098/rspa.2016.0930.

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The formation of pores in anodic aluminium oxide films is treated with a model equation. The model treats the oxide layer as a thin viscous liquid in two dimensions. Surface tension on the top boundary, electrostriction due to the external electric field and mass flow through the bottom boundary due to oxide formation are all included. Viscous flow is treated with the creeping flow assumption. The model equation is solved numerically using a Fourier spectral method in space and Adams–Bashforth/Adams–Moulton methods in time. Initial conditions include sinusoidal shapes as well as random shapes. The results show that pores form at the trough of the initial sinusoidal shape. Random shapes get smoothed before forming pore structures with spacing different than predicted by linear theory.

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Suescún-Díaz, D., M. Narváez-Paredes, and J. H. Lozano-Parada. "Calculation of nuclear reactivity using the generalised Adams-Bashforth-Moulton predictor corrector method." Kerntechnik 81, no. 1 (March 16, 2016): 86–93. http://dx.doi.org/10.3139/124.110591.

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Pan, Yongjun, Yansong He, and Aki Mikkola. "Accurate real-time truck simulation via semirecursive formulation and Adams–Bashforth–Moulton algorithm." Acta Mechanica Sinica 35, no. 3 (February 2, 2019): 641–52. http://dx.doi.org/10.1007/s10409-018-0829-1.

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Lundberg, Bruce N., and Aubrey B. Poore. "Variable Order Adams-Bashforth Predictors with an Error-Stepsize Control for Continuation Methods." SIAM Journal on Scientific and Statistical Computing 12, no. 3 (May 1991): 695–723. http://dx.doi.org/10.1137/0912037.

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Durran, Dale R. "The Third-Order Adams-Bashforth Method: An Attractive Alternative to Leapfrog Time Differencing." Monthly Weather Review 119, no. 3 (March 1991): 702–20. http://dx.doi.org/10.1175/1520-0493(1991)119<0702:ttoabm>2.0.co;2.

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Wicker, Louis J. "A Two-Step Adams–Bashforth–Moulton Split-Explicit Integrator for Compressible Atmospheric Models." Monthly Weather Review 137, no. 10 (October 1, 2009): 3588–95. http://dx.doi.org/10.1175/2009mwr2838.1.

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Abstract Split-explicit integration methods used for the compressible Navier–Stokes equations are now used in a wide variety of numerical models ranging from high-resolution local models to convection-permitting climate simulations. Models are now including more sophisticated and complicated physical processes, such as multimoment microphysics parameterizations, electrification, and dry/aqueous chemistry. A wider range of simulation problems combined with the increasing physics complexity may place a tighter constraint on the model’s time step compared to the fluid flow’s Courant number (e.g., the choice of the integration time step based solely on advective Courant number considerations may generate unacceptable errors associated with the parameterization schemes). The third-order multistage Runge–Kutta scheme has been very successful as the split-explicit integration method; however, its efficiency arises partially in its ability to use a time step that is 20%–40% larger than more traditional integration schemes. In applications in which the time step is constrained by other considerations, alternative integration schemes may be more efficient. Here a two-step third-order Adams–Bashforth–Moulton integrator is stably split in a similar manner as the split Runge–Kutta scheme. For applications in which the large time step is not constrained by the advective Courant number it requires less computational effort. Stability is demonstrated through eigenvalue analysis of the linear coupled one-dimensional velocity–pressure equations, and full two-dimensional nonlinear solutions from a standard test problem are shown to demonstrate solution accuracy and efficiency.

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