A Comparative Study of Numerical Methods for Solving Initial Value Problems (IVP) of Ordinary Differential Equations (ODE)
Year: 2023
Type: article
Abstract: Numerical methods for solving Ordinary Differential Equations differ in accuracy, performance, and applicability. This paper presents a comparative study of numerical methods, mainly Euler’s method, the Runge-Kutta method of order 4th & 6th and the Adams-Bashforth-Moulton method for solving initial value problems in ordinary differential equations. Our aim in this paper is to show that which method gives better accuracy for the initial value problem in numerical methods. Comparisons are made among the direct method, Euler’s method, Runge-Kutta fourth and sixth order and the Adams-Bashforth-Moulton method for solving the initial value problem. The comparisons with error analysis are also shown in the graphical and tabular form. MATHEMATICA 5.2 software is used for programming code and solving the particular problems numerically. It is found that the calculated results for a particular problem using the Runge-Kutta fourth order give good agreement with the exact solution, whereas the Runge-Kutta sixth order defers slightly for a particular problem. Approximate solution using the Adams-Bashforth method with error estimation is also investigated. Moreover, we are also investigated of the Euler methods, the Runge-Kutta methods of order 4th & 6th and the Adams-Bashforth method for solving a particular initial value problem. Finally, it is found that the Adams-Bashforth method gives a better approximation result among the others mentioned methods for solving initial value problems in ordinary differential equations.
Authors: Md. Monirul Islam Sumon, Md. Nurulhoque
Institution: Z. H. Sikder University of Science and Technology
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4389682425