IIARD International Institute of Academic Research and Development

INTERNATIONAL JOURNAL OF APPLIED SCIENCES AND MATHEMATICAL THEORY (IJASMT )

E- ISSN 2489-009X
P- ISSN 2695-1908
VOL. 11 NO. 2 2025
DOI: 10.56201/ijasmt.vol.11.no2.2025.pg11.25

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Bridging Theory and Computation: MATLAB-Based Numerical Methods for Solving Initial Value Problems in Ordinary Differential Equations

Udoh, Ndipmong A, Egbuhuzor, Udechukwu Peter

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Abstract

Numerical methods are very significant as it provides approximate solutions to initial value problems (IVPs) in ordinary differential equations (ODEs) where analytical methods fail. This research work considers the implementation of four widely-used numerical methods: Euler’s Method, Runge-Kutta Fourth-Order Method, Heun’s Method, and Milne’s Predictor-Corrector Method, using MATLAB, a powerful tool for technical computing. This work aims to serve as a practical guide for students and researchers, illustrating the seamless integration of theoretical concepts with computational techniques. It provides a structured framework that can be used for any initial value problems (IVPs) in ordinary differential equations (ODEs). Using a single example problem, we demonstrate the step-by-step MATLAB programming of each method, emphasizing computational efficiency, accuracy and error analysis. This research underscores MATLAB’s capacity to simplify complex numerical computations and offers recommendations for future enhancements. By bridging theoretical foundations and practical applications, this work contributes to the broader understanding and accessibility of numerical methods in scientific computing.

keywords:

Matlab; euler’s method; runge-kutta method; heun’s method; milne’s method

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