Numerical Methods Used for Solving ODE and BVP

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Copyright: 2025
Pages: 31
Source title: ODE, BVP, and 1D PDE Solvers for Scientific and Engineering Problems With MATLAB Basics
Source Author(s)/Editor(s): Leonid Burstein (ORT Braude College of Engineering, Israel (Retired))
DOI: 10.4018/978-1-6684-6850-0.ch005

Keywords: Computer Science & IT / Engineering Science Reference / Programming Languages / Systems and Software Engineering

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Abstract

The chapter presents some numerical methods that are used to solve ODEs when initial conditions (IVP) or conditions at the ends of the solution interval (BVP) are specified. Among the methods discussed are the Euler method, the modified Euler method, the Runge-Kutta method, the BVP finite difference method, and the shooting method. It explains how to use these methods for one or more ODEs. Each method is accompanied by original simple program that solve real ODEs. Various applied problems are solved throughout the chapter and at its end. The problems discussed include solving the Newton's law of cooling, solving the IVP for the water level in the water drain tank, solving the BVP of the I-beam deflection problem, solving the BVP of the temperature distribution of a moving rod, and others.

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