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Journal articles on the topic 'Adams-Bashforth method'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

Apriani, Dewi, Wasono Wasono, and Moh Nurul Huda. "Penerapan Metode Adams-Bashforth-Moulton pada Persamaan Logistik Dalam Memprediksi Pertumbuhan Penduduk di Provinsi Kalimantan Timur." EKSPONENSIAL 13, no. 2 (2022): 95. http://dx.doi.org/10.30872/eksponensial.v13i2.1046.

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Logistic equation is a nonlinear ordinary differential equation that describes the population. Nonlinear ordinary differential equations can be solved by one of the numerical methods, namely the Adams-Bashforth-Moulton method. Adams-Bashforth-Moulton method is a multistep method which consists of Adams-Bashforth method as predictor and Adams-Moulton method as corrector. The logistic equation is solved first by using the Runge-Kutta method to obtain the four initial solutions, then followed by the Adams-bashforth-Moulton method. This study aims to predict population growth in the province of Ea

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Soomro, Paras, Israr Ahmed, Faraz Ahmed Soomro, and Darshan Mal. "Numerical Simulation Model of the Infectious Diseases by Comparing Backward Euler Method and Adams-Bash forth 2-Step Method." VFAST Transactions on Mathematics 12, no. 1 (2024): 402–14. http://dx.doi.org/10.21015/vtm.v12i1.1881.

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In this work, the Backward Euler technique and the Adams-Bashforth 2-step method—two numerical approaches for solving the SIR model of epidemiology are compared for performance. An essential resource for comprehending the transmission of infectious illnesses like COVID-19 in the SIR model. While the explicit Adams-Bash forth 2-step approach is well known for its computing efficiency, the implicit Backward Euler method is noted for its stability. The study evaluates the accuracy, strength, and computing cost of the two approaches to determine which approach is best for simulating the spread of

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3

Alorgbey, Bernard, Sumarni Abdullah, Paul Kahenya Njoroge, and Yusra Rewili. "Application of Adams-Bashforth-Moulton Method on Logistic Equation in Predicting Population Growth." Interval: Indonesian Journal of Mathematical Education 3, no. 1 (2025): 82–94. https://doi.org/10.37251/ijome.v3i1.1595.

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Purpose of the study: This study aims to obtain population growth prediction results using the Adams-Bashforth-Moulton method. Methodology: This type of research is applied research. In this study, the Adams-Bashforth-Moulton method was applied by solving the problem of population growth in South Sulawesi Province. Main Findings: The logistic equation for population growth with a step size of h = 1 and the capacity of South Sulawesi Province is 20,000,000 people, with a growth rate of 2%. The numerical solution of the logistic equation for population growth at time t = 2020 with an optimal ste

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4

Balogun, Ometere Deborah, Israel Oluwarotimi Oluwafemi, and Olamigoke Emmanuel Famakinwa. "Review of Adams-Bashforth method for numerical solution of first order ordinary differential equations." Global Journal of Engineering and Technology Advances 19, no. 1 (2024): 037–61. https://doi.org/10.5281/zenodo.13690205.

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This project work presents a comprehensive review of the Adams-Bashforth method for the numerical solution of explicit first-order ordinary differential equations (ODEs). The study begins with a historical overview of the development of ordinary differential equations (ODEs), tracing back to the seminal works of Newton, Leibniz, and their contemporaries. The evolution of differential equations as a distinct mathematical discipline and their wide-ranging applications across various fields are discussed. Furthermore, the paper provides an in-depth analysis of the Adams-Bashforth method, a promin

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Tarisma, Tantri, Fazrina Saumi, and Ulya Nabilla. "Application Of The Adams Bashforth-Moulton Method To Coffee Production Quantity Approach." Mathline : Jurnal Matematika dan Pendidikan Matematika 9, no. 4 (2024): 1063–71. https://doi.org/10.31943/mathline.v9i4.660.

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Coffee is a type of plantation plant that has long been cultivated so that it has high economic value. Therefore, the authors are interested in approximating the amount of coffee production using the Adams Basforth Moulton method. The Adams Bashforth Moulton method is a way of finding a numerical solution at a certain point of a non-linear differential equation with a known initial value. The differential equation is first solved using the fourth-order Runge Kutta method to obtain four initial solutions which are then substituted into the fourth order Adams Bashforth predictor equation. Furthe

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Silvy Faiza Ryadi, Gani Gunawan, and Yani Ramdani. "Penerapan Metode Adams Bashforth Moulton pada Persamaan Logistik untuk Memprediksi Pertumbuhan Ekonomi Jawa Barat." Bandung Conference Series: Mathematics 4, no. 1 (2024): 12–20. http://dx.doi.org/10.29313/bcsm.v4i1.15296.

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Abstract. This research is about the application of the Adams Bashforth Moulton method to predict economic growth in West Java using the logistic equation. The logistic equation which is a population growth model is used to predict economic growth because according to Adams Smith theory, economic growth actually relies on population growth. The logistic equation is derived to obtain a logistic model in the form of a differential equation whose solution can use the Adams Bashforth Moulton method. The 4th Order Runge-Kutta method is used to obtain the initial solution needed in the Adams Bashfor

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7

Balogun Ometere Deborah, Oluwafemi Israel Oluwarotimi, and Famakinwa Olamigoke Emmanuel. "Review of Adams-Bashforth method for numerical solution of first order ordinary differential equations." Global Journal of Engineering and Technology Advances 19, no. 1 (2024): 037–61. http://dx.doi.org/10.30574/gjeta.2024.19.1.0056.

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This project work presents a comprehensive review of the Adams-Bashforth method for the numerical solution of explicit first-order ordinary differential equations (ODEs). The study begins with a historical overview of the development of ordinary differential equations (ODEs), tracing back to the seminal works of Newton, Leibniz, and their contemporaries. The evolution of differential equations as a distinct mathematical discipline and their wide-ranging applications across various fields are discussed. Furthermore, the paper provides an in-depth analysis of the Adams-Bashforth method, a promin

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8

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

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9

Odeyemi, J. K., O. O. Olaiya, and F. O. Ogunfiditimi. "Hermite Polynomial-based Methods for Optimal Order Approximation of First-order Ordinary Differential Equations." Journal of Advances in Mathematics and Computer Science 38, no. 6 (2023): 16–32. http://dx.doi.org/10.9734/jamcs/2023/v38i61765.

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This study investigates the continuous linear multistep techniques utilized for solving first-order initial value problems in ordinary differential equations. Specifically, the study focuses on step k = 9, utilizing Hermite polynomials as basis functions. This study effectively constructs the Adams-Bashforth, Adams-Moulton, and optimal order methods by applying collocation and interpolation methodologies. The methods are thoroughly examined using various numerical instances to demonstrate their efficacy and validity. Notably, the optimal order method exhibits superior accuracy and efficiency c

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Muhammad Abdy and Irwan Irwan. "Solusi Numerik Model Matematika SIPAS dalam Penyebaran Praktik Monkey Business dengan Metode Adams-Bashforth-Moulton." Journal of Mathematics: Theory and Applications 6, no. 1 (2024): 114–23. http://dx.doi.org/10.31605/jomta.v6i1.3721.

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This research is applied research to determine the numerical solution for the SIPAS mathematical model for the spread of monkey business practices using the Adams-Bashforth-Moulton method. The epidemic model for the spread of monkey business practices is susceptible, infected, practiced, and awareness (SIPAS). The discussion begins by determining the initial solution using the fifth order Runge-Kutta method, prediction and correction values using the Adams-Bashforth-Moulton method, simulation and analysis of the results. In this research, it was found that the Adams-Bashforth- Moulton method p

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11

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

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12

Zhang, Chong, Pengbo Qin, Qingtian Lü, Wenna Zhou, and Jiayong Yan. "Two New Methods Based on Implicit Expressions and Corresponding Predictor-Correctors for Gravity Anomaly Downward Continuation and Their Comparison." Remote Sensing 15, no. 10 (2023): 2698. http://dx.doi.org/10.3390/rs15102698.

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Downward continuation is a key technique for processing and interpreting gravity anomalies, as it has a major role in reducing values to horizontal planes and identifying small and shallow sources. However, it can be unstable and inaccurate, particularly when continuation depth increases. While the Milne and Adams–Bashforth methods based on numerical solutions of the mean-value theorem have partly addressed these problems, more accurate and realistic methods need to be presented to enhance results. To address these challenges, we present two new methods, Milne–Simpson and Adams–Bashforth–Moult

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13

Kumar, Sunil, Ali Ahmadian, Ranbir Kumar, et al. "An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets." Mathematics 8, no. 4 (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 a

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14

Farah Liyana Azizan, Saratha Sathasivam, Muraly Velavan, Nur Rusyidah Azri, and Nur Iffah Rafhanah Abdul Manaf. "Prediction of Drug Concentration in Human Bloodstream using Adams-Bashforth-Moulton Method." Journal of Advanced Research in Applied Sciences and Engineering Technology 29, no. 2 (2023): 53–71. http://dx.doi.org/10.37934/araset.29.2.5371.

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Pharmaceutical drugs are chemicals intended to avoid, assess, heal, or cure a disease. It is also commonly referred to as medication. When medicine is taken, it gets absorbed into the bloodstream, spreads throughout the body, and achieves its maximum concentration. Following this, the medication level gradually decreases as it is removed from the body. The drug concentration according to the time can be predicted using mathematical concepts and pharmacokinetic models. The compartmental model is a fundamental type of model used in pharmacokinetics. The number of compartments required to describ

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15

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 i

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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 (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

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17

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 (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

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18

Marasi, H. R., M. H. Derakhshan, A. Soltani Joujehi, and Pushpendra Kumar. "Higher-order fractional linear multi-step methods." Physica Scripta 98, no. 2 (2023): 024004. http://dx.doi.org/10.1088/1402-4896/acad42.

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Abstract In this paper, we propose two arrays, containing the coefficients of fractional Adams-Bashforth and Adams-Moulton methods, and also recursive relations to produce the elements of these arrays. Then, we illustrate the application of these arrays in a suitable way to construct higher-order fractional linear multi-step methods in general form, with extended stability regions. The effectiveness of the new method is shown in comparison with some available previous results in an illustrative test problem.

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Gajewski, Andrzej, and Tomasz Janusz Teleszewski. "A New Method for Determining Interfacial Tension: Verification and Validation." Energies 16, no. 2 (2023): 613. http://dx.doi.org/10.3390/en16020613.

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Surface tension is a meaningful parameter influencing boiling and condensation in macroscopic scale, in confined spaces, or for nanofluids; it further affects boiling with surfactants. Surface, or interfacial, tension is an important property in the research into increasing heat transfer, enhancing efficiency of photovoltaic systems, improving engine operation, or forming drugs or polymers. It is often determined using axisymmetric drop shape analysis based on the differential equations system formulated by Bashforth and Adams. The closed-form expression of the interface shape states the radii

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Samia Atallah. "The Numerical Methods of Fractional Differential Equations." مجلة جامعة بني وليد للعلوم الإنسانية والتطبيقية 8, no. 4 (2023): 496–512. http://dx.doi.org/10.58916/jhas.v8i4.44.

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Differential equations with non-integer order derivatives have demonstrated are suitable models for a variety of physical events in several fields including diffusion processes and damping laws, fluid mechanics neural networks. In this study, i will discuss two numerical methods Diethelm's method and Adams-Bashforth-Moulton method for solving fractional ordinary differential equations (ODEs) with initial conditions.

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Kuzairi, Kuzairi, Tony Yulianto, and Lilik Safitri. "APLIKASI METODE ADAMS BASHFORTH-MOULTON (ABM) PADA MODEL PENYAKIT KANKER." Jurnal Matematika "MANTIK" 2, no. 1 (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 A

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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 (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 solvin

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Azhar, Aurizan Himmi, Sugiyanto Sugiyanto, Muhammad Wakhid Musthofa, and Muhamad Zaki Riyanto. "Transformasi Fourier Multiplikatif Dan Aplikasinya Pada Persamaan Diferensial Multiplikatif." Jurnal Derivat: Jurnal Matematika dan Pendidikan Matematika 8, no. 2 (2021): 149–60. http://dx.doi.org/10.31316/j.derivat.v8i2.1996.

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This research is a development of multiplicative calculus. This study is about the Fourier multiplicative transformation and its application to the multiplicative differential equation. This study aims to determine the Fourier multiplicative transformation as well as the multiplicative differential equation. This study contains numerical simulations to solve the problem of ordinary multiplicative differential equations of the first order. The methods used in this research are descriptive research methods through the study of literature. The results of this study are the application of multipli

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Rosu, Florin. "Parallel Algorithm for Numerical Methods Applied to Fractional-order System." Scalable Computing: Practice and Experience 21, no. 4 (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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Melliani, Said, Fouziya Zamtain, M'hamed Elomari, and Lalla Saadia Chadli. "Solving fuzzy fractional Atangana-Baleanu differential equation using Adams-Bashforth-Moulton method." Boletim da Sociedade Paranaense de Matemática 41 (December 28, 2022): 1–12. http://dx.doi.org/10.5269/bspm.63335.

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This work is concerned with the numerical study of the fuzzy fractional equation involving the Atangana-Baleanu derivative in the sense of Caputo. We are going to apply the Adams Bashforth Moulton method to the equation concerned, which is an interconnection between the Lagrange approximation and the trapezoidal rule. We achieved this work by giving examples that illustrate this method.

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MAZZONE, A. M. "VERLET METHODS WITH STEPSIZE CONTROL FOR MOLECULAR DYNAMICS CALCULATIONS." International Journal of Modern Physics C 12, no. 01 (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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Sadikin, Zubaidah, Zaileha Md Ali, Fatin Nadira Rusly, Nuramira Husna Abu Hassan, Siti Rahimah Batcha, and Noratika Nordin. "SIR FRACTIONAL ORDER OF COVID-19 by ADAMS BASHFORTH-MOULTON METHOD." MALAYSIAN JOURNAL OF COMPUTING (MJOC) 9, no. 1 (2024): 1690–705. http://dx.doi.org/10.24191/mjoc.v9i1.24439.

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This study addresses a research gap by introducing fractional order derivatives into the SIR model for tracking COVID-19 in Malaysia. The Caputo sense fractional derivative and the Adams Bashforth Moulton method are employed to analyse the COVID-19 behavior and stability. By manipulating fractional order derivative values, this study investigates their impact on key SIR parameters, observing that lower values accelerate the attainment of asymptotic behavior in populations. The stability analysis reveals two equilibrium points: an unstable disease-free equilibrium and a stable endemic equilibri

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Danca, Marius-F., and Nikolay Kuznetsov. "Matlab Code for Lyapunov Exponents of Fractional-Order Systems." International Journal of Bifurcation and Chaos 28, no. 05 (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 Mat

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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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Jeng, Siow W., and Adem Kilicman. "Fractional Riccati Equation and Its Applications to Rough Heston Model Using Numerical Methods." Symmetry 12, no. 6 (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 mode

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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 (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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Safikhani, Leila, Tofigh Allahviranloo, Leo Mrsic, and Sovan Samanta. "Numerical Solution for Fuzzy Fractional Differential Equations by Fuzzy Multi-Step Methods." Symmetry 17, no. 4 (2025): 545. https://doi.org/10.3390/sym17040545.

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To solve fractional differential equations, they are typically converted into their corresponding crisp problems through a process known as the embedding method. This paper introduces a novel direct approach to solving fuzzy differential equations using fuzzy calculations, bypassing the need for this transformation. In this study, we develop the fuzzy Adams–Bashforth (A-B) method and the fuzzy Adams–Moulton (A-M) method to find numerical solutions for fuzzy fractional differential equations (FFDEs) with fuzzy initial values. To demonstrate the accuracy and efficiency of the proposed methods, w

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Yucedag, Vedat Burak, and Ilker Dalkiran. "A Raspberry Pi-based Hardware Implementation of Various Neuron Models." Elektronika ir Elektrotechnika 30, no. 6 (2024): 19–28. https://doi.org/10.5755/j02.eie.38201.

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The implementation of biological neuron models plays an important role in understanding the functionality of the brain. Generally, analog and digital methods are preferred during implementation processes. The Raspberry Pi (RPi) microcontroller has the potential to be a new platform that can easily solve complex mathematical operations and does not have memory limitations, which will take advantage while realizing biological neuron models. In this paper, Hodgkin-Huxley (HH), FitzHugh-Nagumo (FHN), Morris-Lecar (ML), Hindmarsh-Rose (HR), and Izhikevich (IZ) neuron models have been implemented on

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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 (2017): 674–77. http://dx.doi.org/10.3139/124.110842.

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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 (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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Nor Solehah Sanik, Nur Fatihah Fauzi, Nurizatul Syarfinas Ahmad Bakhtiar, Huda Zuhrah Ab. Halim, Nur Izzati Khairudin, and Nor Hayati Shafii. "Comparison of The Trapezoidal and Adam Bashforth Approaches in The Lotka-Volterra Prey-Predator Dynamics." Applied Mathematics and Computational Intelligence (AMCI) 13, no. 4 (2024): 91–102. http://dx.doi.org/10.58915/amci.v13i4.1484.

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This study primarily focuses on comparing the numerical methods of the Adams-Bashforth and Trapezoidal methods with the exact solution for solving the Lotka-Volterra prey-predator model. These methods are evaluated for their ability to reliably and accurately solve the non-linearity of the model. Based on the results, both methods offer precise solutions, with the Adams-Bashforth method providing a more accurate approximation for short-term predictions and the Trapezoidal method demonstrating better stability for long-term simulations. The study utilizes data from lynx-rabbit and bat-moth inte

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Wang, Zhen. "A Numerical Method for Delayed Fractional-Order Differential Equations." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/256071.

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A numerical method for nonlinear fractional-order differential equations with constant or time-varying delay is devised. The order here is an arbitrary positive real number, and the differential operator is with the Caputo definition. The general Adams-Bashforth-Moulton method combined with the linear interpolation method is employed to approximate the delayed fractional-order differential equations. Meanwhile, the detailed error analysis for this algorithm is given. In order to compare with the exact analytical solution, a numerical example is provided to illustrate the effectiveness of the p

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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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Dong, Jian, Jianliang Hu, Zihao Zhang, Mengying Gong, and Zhixin Li. "Predictions of the Wettable Parameters of an Axisymmetric Large-Volume Droplet on a Microstructured Surface in Gravity." Micromachines 14, no. 2 (2023): 484. http://dx.doi.org/10.3390/mi14020484.

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In this study, a numerical model was developed to predict the wettable parameters of an axisymmetric large-volume droplet on a microstructured surface in gravity. We defined a droplet with the Bond number Bo>0.1 as a large-volume droplet. Bo was calculated by using the equation Bo=ρlgγlv3V4π23 where ρl is the density of liquid, γlv is the liquid-vapor interfacial tension, g is the gravity acceleration and V is the droplet volume. The volume of a large-volume water droplet was larger than 2.7 μL. By using the total energy minimization and the arc differential method of the Bashforth–Adams eq

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Egbetade, Samuel Adeleye, and Abimbola Latifat Adebisi. "NUMERICAL SOLUTION OF FIRST AND SECOND ORDER DIFFERENTIAL EQUATIONS USING THE TAU METHOD WITH AN ESTIMATION OF THE ERROR." FUDMA JOURNAL OF SCIENCES 9, no. 3 (2025): 119–21. https://doi.org/10.33003/fjs-2025-0903-3346.

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The Subject of Numerical methods is an important aspect of ordinary differential equations. It is useful in providing solutions to a wide variety of complex differential equations arising from engineering, physical and biological sciences, health and other allied disciplines which are difficult to tackle by exact methods. Numerical approximations of differential equations of one and higher order have been provided using Euler Method, Tau Method, Runge-Kutta Method, Adams-Bashforth Method, Milne Simpson predictor-corrector Method, Adams-Moulton linear multistep method and a host of others. In t

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Mahatekar, Yogita, Pallavi S. Scindia, and Pushpendra Kumar. "A new numerical method to solve fractional differential equations in terms of Caputo-Fabrizio derivatives." Physica Scripta 98, no. 2 (2023): 024001. http://dx.doi.org/10.1088/1402-4896/acaf1a.

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Abstract In this article, we derive a new numerical method to solve fractional differential equations containing Caputo-Fabrizio derivatives. The fundamental concepts of fractional calculus, numerical analysis, and fixed point theory form the basis of this study. Along with the derivation of the algorithm of the proposed method, error and stability analyses are performed briefly. To explore the validity and effectiveness of the proposed method, several examples are simulated, and the new solutions are compared with the outputs of the previously published two-step Adams-Bashforth method.

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Kapçiu, Rinela, Brikena Preni, Eglantina Kalluçi, and Robert Kosova. "MODELING INFLATION DYNAMICS USING THE LOGISTIC MODEL: INSIGHTS AND FINDINGS." Jurnal Ilmiah Ilmu Terapan Universitas Jambi 8, no. 1 (2024): 364–78. http://dx.doi.org/10.22437/jiituj.v8i1.32605.

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This paper examines applying the logistic model, frequently used in biology, to analyze inflation patterns in dynamic economic systems. The primary objective is to simulate and analyze the complex dynamics of inflation, thus providing new insights into the stability of financial institutions. Numerical methods such as Euler's Method, Runge-Kutta Method (RK4), and Adams-Bashforth-Moulton's method were used to simulate inflation patterns by discretizing the logistic equation. The data utilized in this research were obtained from INSTAT, BoA, MoF, and Eurostat, with quarterly results from 1995 to

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Zaileha Md Ali, Fatin Nadira Rusly, Nuramira Husna Abu Hassan, Nur Aziean Mohd Idris, Siti Rahimah Batcha, and Zubaidah Sadikin. "SIR Fractional Order of Simulated Covid-19 Cases using Adams Bashforth-Moulton Method." Journal of Advanced Research in Applied Sciences and Engineering Technology 42, no. 1 (2024): 82–92. http://dx.doi.org/10.37934/araset.42.1.8292.

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Fractional order derivative has been widely used in many different areas such as bioengineering, fluid mechanics, circuits systems, biomathematics, and biomedicine. This study introduces the system of the fractional differential equation on SIR (Susceptible-Infected-Recovered) model to simulate the COVID-19 in Malaysia. The fractional derivative is described in Caputo sense and solved by the Adams Bashforth Moulton method. The Runge-Kutta method is used to prove and validate the numerical results obtained. The graphical representations of the simulation with difference fractional order have be

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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 (2016): 86–93. http://dx.doi.org/10.3139/124.110591.

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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 (1991): 702–20. http://dx.doi.org/10.1175/1520-0493(1991)119<0702:ttoabm>2.0.co;2.

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Olatunji, Oladayo, and Adeyemi Akeju. "Comparative Analysis of Euler and Order Four Runge-Kutta Methods in Adams-Bashforth-Moulton Predictor-Corrector Method." International Journal of Mathematics, Statistics, and Computer Science 3 (January 2, 2025): 276–93. https://doi.org/10.59543/ijmscs.v3i.10471.

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This study conducts a comparative analysis of the Euler and Runge-Kutta 4 methods within the Adams Predictor-Corrector frameworkfor solving second-order ordinary differential equations (ODEs) andcoupled differential equations. The Euler method, a basic first-orderexplicit scheme, and the Runge-Kutta 4 method, a higher-order ex-plicit scheme, are widely utilized numerical methods for ODEs. How-ever, their effectiveness varies based on the problem’s characteristics.We specifically investigate these methods integrated into the AdamsPredictor-Corrector method, renowned for its stability and effici

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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 (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: Ada

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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 (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.

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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 (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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Salih, M. M., and F. Ismail. "Trigonometrically-Fitted Fifth Order Four-Step Predictor-Corrector Method for Solving Linear Ordinary Differential Equations with Oscillatory Solutions." Malaysian Journal of Mathematical Sciences 16, no. 4 (2022): 739–48. http://dx.doi.org/10.47836/mjms.16.4.07.

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In this paper, we proposed a trigonometrically-fitted fifth order four-step predictor-corrector method based on the four-step Adams-Bashforth method as predictor and five-step Adams-Moulton method as corrector to solve linear ordinary differential equations with oscillatory solutions. This method is constructed which exactly integrate initial value problems whose solutions can be expressed as linear combinations of the set functions {sin(υx),cos(υx)} with υ ∈ R, where v represents an approximation of the frequency of the problem. The frequency will be used in the method to raise the accuracy o

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