Relevant bibliographies by topics / Adams-Bashforth

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Academic literature on the topic 'Adams-Bashforth'

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Published: 4 June 2021
Last updated: 14 February 2022

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Journal articles on the topic "Adams-Bashforth"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Adams-Bashforth"

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Allampalli, Vasanth. "Fourth order Multi-Time-Stepping Adams-Bashforth (MTSAB) scheme for NASA Glenn Research Center's Broadband Aeroacoustic Stator Simulation (BASS) Code." Toledo, Ohio : University of Toledo, 2010. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=toledo1270739741.

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Dissertation (Ph.D.)--University of Toledo, 2010.
Typescript. "Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Doctor of Philosophy Degree in Engineering." "A dissertation entitled"--at head of title. Title from title page of PDF document. Bibliography: p. 152-156.
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Allampalli, Vasanth. "Fourth order Multi-Time-Stepping Adams-Bashforth (MTSAB) scheme for NASA Glenn Research Center’s Broadband Aeroacoustic Stator Simulation (BASS) Code." University of Toledo / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1270739741.

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Alzahrani, Abdulrahman. "Contractivity-Preserving Explicit 2-Step, 6-Stage, 6-Derivative Hermite-Birkhoff–Obrechkoff Ode Solver of Order 13." Thesis, Université d'Ottawa / University of Ottawa, 2015. http://hdl.handle.net/10393/32564.

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In this thesis, we construct a new optimal contractivity-preserving (CP) explicit, 2-step, 6-stage, 6-derivative, Hermite--Birkhoff--Obrechkoff method of order 13, denoted by HBO(13) with nonnegative coefficients, for solving nonstiff first-order initial value problems y'=f(t,y), y(t_0)=y_0. This new method is the combination of a CP 2-step, 6-derivative, Hermite--Obrechkoff of order 9, denoted by HO(9), and a 6-stage Runge-Kutta method of order 5, denoted by RK(6,5). The new HBO(13) method has order 13. We compare this new method, programmed in Matlab, to Adams-Bashforth-Moulton method of order 13 in PECE mode, denoted by ABM(13), by testing them on several frequently used test problems, and show that HBO(13) is more efficient with respect to the CPU time, the global error at the endpoint of integration and the relative energy error. We show that the new HBO(13) method has a larger scaled interval of absolute stability than ABM(13) in PECE mode.
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Kluknavský, František. "Vliv přesnosti aritmetických operací na přesnost numerických metod." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2012. http://www.nusl.cz/ntk/nusl-236465.

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Thesis is dedicated to evaluation of roundoff impact on numerical integration methods accuracy and effectivity. Contains theoretical expectations taken from existing literature, implementation of chosen methods, experimental measurement of attained accuracy under different circumstances and their comparison with regard to time complexity. Library contains Runge-Kutta methods to order 7 and Adams-Bashforth methods to order 20 implemented using C++ templates which allow optional arbitrary-precision arithmetic. Small models with known analytic solution were used for experiments.
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Platte, Rodrigo Barcelos. "Simulação em variáveis primitivas de escoamento incompressíveis com atualizacao direta e explícita para pressão." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 1998. http://hdl.handle.net/10183/127336.

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No presente trabalho estudam-se diferentes técnicas explícitas, em diferenças finitas, no emprego de algoritmos do tipo velocidade-pressão para simulação de escoamentos incompressíveis. O método de resolução da pressão de maneira direta e explícita, introduzido por Bravo e Claeyssen [BRA 97a], é analisado. Faz-se uma aproximação para o erro causado por esta técnica, e verifica-se como isto afeta a equação da continuidade. As simulações são realizadas na cavidade quadrada, comparando-se os diferentes métodos e validando as aproximações realizadas no estudo do método de resolução da pressão. Além disso, simula-se o escoamento em cavidades profundas e rasas, observandose a formação de vórtices e distribuição de energia cinética. Simulações do escoamento na cavidade cúbica também são apresentadas.
In this work different explicit technics in finite defferences in the application of velocity-pressure algorithm to simulate incompressible flows have been studied. The direct and explicit method of pressure resolution, introduced by Bravo anel Claeyssen [BRA 97a] is analyzed. An approximation to the error caused by this method is made, anel how this affects the continuity equation is verified. The simulations are maele in a square cavity, comparing the differents methoels anel valielating the approximations maele in the study of the pressure resolution method. Besieles this, flow in eleep and shallow cavities is simulateel, observing the formation of vortices and kinetic energy distribution. Simulations of the flow in the cubical cavity are also considered.
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Sibiya, Abram Hlophane. "Numerical methods for a four dimensional hyperchaotic system with applications." Diss., 2019. http://hdl.handle.net/10500/26398.

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This study seeks to develop a method that generalises the use of Adams-Bashforth to solve or treat partial differential equations with local and non-local differentiation by deriving a two-step Adams-Bashforth numerical scheme in Laplace space. The resulting solution is then transformed back into the real space by using the inverse Laplace transform. This is a powerful numerical algorithm for fractional order derivative. The error analysis for the method is studied and presented. The numerical simulations of the method as applied to the four-dimensional model, Caputo-Lu-Chen model and the wave equation are presented. In the analysis, the bifurcation dynamics are discussed and the periodic doubling processes that eventually caused chaotic behaviour (butterfly attractor) are shown. The related graphical simulations that show the existence of fractal structure that is characterised by chaos and usually called strange attractors are provided. For the Caputo-Lu-Chen model, graphical simulations have been realised in both integer and fractional derivative orders.
Mathematical Sciences
M. Sc. (Applied Mathematics)
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Books on the topic "Adams-Bashforth"

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Wood, M. B. An improved Adams-Bashforth numerical integration routine. London: HMSO, 1992.

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Book chapters on the topic "Adams-Bashforth"

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Korch, Matthias. "Locality Improvement of Data-Parallel Adams–Bashforth Methods through Block-Based Pipelining of Time Steps." In Euro-Par 2012 Parallel Processing, 563–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-32820-6_56.

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Psihoyios, G., and T. E. Simos. "Trigonometrically fitted Adams-Bashforth-Moulton methods for periodic initial value problems." In Computational Fluid and Solid Mechanics 2003, 2097–100. Elsevier, 2003. http://dx.doi.org/10.1016/b978-008044046-0.50515-7.

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Glatzmaier, Gary A. "Numerical Method." In Introduction to Modeling Convection in Planets and Stars. Princeton University Press, 2013. http://dx.doi.org/10.23943/princeton/9780691141725.003.0002.

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This chapter describes a numerical method for solving equations of thermal convection on a computer. It begins by introducing the vorticity-streamfunction formulation as a means of conserving mass. The approach involves updating for the vorticity first and then solving for the fluid velocity each time step. The chapter continues with a discussion of two very different spatial discretizations, whereby the vertical derivatives are approximated with a finite-difference method and the horizontal derivatives with a spectral method. The nonlinear terms are computed in spectral space. The chapter also considers the Adams-Bashforth time integration scheme and explains how the Poisson equation can be solved at each time step for the updated streamfunction given the updated vorticity.
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"FIG. 10 Shape of the liquid droplet from the numerical tables of Bashforth and Adams [29] for β=1. The location of the substrate (the broken horizontal line) is such that the liquid-vapor surface meets the substrate with angle θ." In Surface and Interfacial Tension, 177–79. CRC Press, 2004. http://dx.doi.org/10.1201/9780203021262-61.

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Conference papers on the topic "Adams-Bashforth"

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Nutaro, James. "A Second Order Accurate Adams-Bashforth Type Discrete Event Integration Scheme." In 21st International Workshop on Principles of Advanced and Distributed Simulation. IEEE, 2007. http://dx.doi.org/10.1109/pads.2007.9.

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Mesˇtrovic´, Mladen. "An Application of Modified Predictor-Corrector Method." In ASME/JSME 2004 Pressure Vessels and Piping Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/pvp2004-2773.

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The explicit numerical integration method, introduced and proposed in the paper given by Chiou and Wu [1], is further developed. The method is based on the relationship that m-step Adams-Moulton method is linear convex combination of the (m − 1)-step Adams-Moulton and m-step Adams-Bashforth method with a fixed weighting coefficients. The general form taken from Chiou and Wu [1] is used to evaluate the recurrence expressions using the different number of previous mesh points. The explicit expressions are given for modified 3-step predictor-corrector method. The numerical algorithms are given for first and second-order nonlinear initial value problems and for system of ordinary differential equations. Some numerical examples, for different kind of problems, are used to demonstrate the efficiency and the accuracy of the proposed numerical method. The calculated numerical solutions show superiority of presented modified predictor-corrector method to standard Adams-Bashforth-Moulton predictor-corrector method.
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Allampalli, Vasanth, and Ray Hixon. "Implementation of Multi-Time Step Adams-Bashforth Time Marching Scheme for CAA." In 46th AIAA Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2008. http://dx.doi.org/10.2514/6.2008-29.

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Bohlen, T., and F. Wittkamp. "Higher Order FDTD Seismic Modelling Using the Staggered Adams-Bashforth Time Integrator." In 77th EAGE Conference and Exhibition 2015. Netherlands: EAGE Publications BV, 2015. http://dx.doi.org/10.3997/2214-4609.201412836.

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Xiao, Feng, Ming Yuchi, Ming-yue Ding, Jun Jo, and Jong-Hwan Kim. "A multi-step heart rate prediction method based on physical activity using Adams-Bashforth technique." In 2009 IEEE International Symposium on Computational Intelligence in Robotics and Automation - (CIRA 2009). IEEE, 2009. http://dx.doi.org/10.1109/cira.2009.5423181.

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Blasik, Marek. "A variant of Adams — Bashforth — Moulton method to solve fractional ordinary differential equation." In 2015 20th International Conference on Methods and Models in Automation and Robotics (MMAR ). IEEE, 2015. http://dx.doi.org/10.1109/mmar.2015.7284045.

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Blasik, Marek. "A new variant of Adams — Bashforth — Moulton method to solve sequential fractional ordinary differential equation." In 2016 21st International Conference on Methods and Models in Automation and Robotics (MMAR). IEEE, 2016. http://dx.doi.org/10.1109/mmar.2016.7575249.

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Poguluri, Sunny Kumar, Krishnankutty Parameswaran, and Vendhan Chiruvai Pattu. "A Study of Adams-Bashforth Method in the Finite Element Based Model for Nonlinear Water Waves." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-66006.

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The problem of nonlinear water waves, which is of great practical importance in ocean engineering, has been studied vigorously for over three decades by adopting a Mixed Eulerian-Lagrangian (MEL) formulation that employs the fully nonlinear potential flow theory (FNPT). In this approach, the free surface equations in the Lagrangian frame are solved using a time marching procedure and the Laplace equation in the fluid domain is solved in the Eulerian frame. While the boundary integral/element method for solving the Laplace equation has been studied for over 4 decades, the finite element (FE) method has been investigated during the last 2 decades. Time domain (TD) integration of the free surface equations in the MEL model is a crucial step. In the FE based MEL model, FE solution of the Laplace equation, which is the most computationally intensive part, is required at each time step. The fourth order Runge-Kutta (RK4) method, which involves four function evaluations at each time step, has been widely used for solving the free surface equations. In this context, the third and fourth order Adams-Bashforth (AB3 & AB4) methods that involve only one function evaluation at each time step are worth considering. For a chosen time step, the RK4 method is much more accurate than the AB methods, in addition to having much better stability. So, it is essential to study the performance of the AB methods from the view point of accuracy and stability, with a focus on computational economy. In the present paper, such a study has been undertaken employing a MEL computation capability recently developed by the authors. Since the accuracy of MEL solution to sloshing problems is not hindered by radiation boundary condition (r.b.c.), it has been adopted here to carry out simulations over several wave cycles. Since long-time nonlinear simulations using the MEL formulation are generally hampered by instability, the case of small amplitude sloshing has been simulated for about 1000 wave cycles using the AB3 and AB4 algorithms. In the MEL numerical model, errors accrue at every time step because of numerical integration, FE solution of the Laplace equation and estimation of velocities using the FE solution. The errors in the amplitude and phase of free surface waves have been estimated and compared for different simulations. The errors in the FE solution at every time step, which is an input for the next time stepping calculation, appear contained and no solution instability has been noticed. As a second example, nonlinear sloshing with a moderate steepness of 1/30 has been considered. For this case, simulations could not be carried out beyond about 30 to 50 cycles, because of the well known saw-tooth instability associated with the Lagrangian model for the free surface equations. This instability manifests as Jacobian determinant error in the isoparametric element formulation. Interestingly, this seems to provide a diagnostic to detect saw-tooth instability in the MEL model. It would be useful to develop accurate smoothing techniques to overcome this instability and also extend the computation capability to problems with higher wave steepness.
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Fathoni, Muhammad Faris, and Aciek Ida Wuryandari. "Comparison between Euler, Heun, Runge-Kutta and Adams-Bashforth-Moulton integration methods in the particle dynamic simulation." In 2015 4th International Conference on Interactive Digital Media (ICIDM). IEEE, 2015. http://dx.doi.org/10.1109/idm.2015.7516314.

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Ingraham, Daniel, Vasanth Allampalli, and Ray Hixon. "Verification of a Multi-Time-Step Adams-Bashforth (MTSAB) Time-Marching Scheme Using External Verification Analysis (EVA)." In 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2011. http://dx.doi.org/10.2514/6.2011-1088.

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