Implementation of the forward Euler method in MATLAB

Zhaoran Guo; Shaobo Wang

doi:10.1117/12.2628077

22 April 2022 Implementation of the forward Euler method in MATLAB

Zhaoran Guo, Shaobo Wang

Proceedings Volume 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021); 121632T (2022) https://doi.org/10.1117/12.2628077
Event: International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 2021, Nanjing, China

Abstract

For some simple differential equations, it is possible to calculate exact expressions for a solution. However, for most of the differential equations, it is impossible to obtain their closed-form solutions. Our purpose is to make an approximation to solutions of differential equations, i.e., to look for a function (or some discrete approximation to this function) satisfying a given relationship between various of its derivatives on some given domain of space and/or time with some boundary conditions. Generally, only rarely can an analytic formula be found for the solution. A finite difference method proceeds by replacing the derivatives in the differential equations with finite difference approximations. In this paper, we mainly focus on the forward Euler method and its implementation. We show how to solve the ordinary differential equations by the forward Euler's algorithm through two instances.

Citation Download Citation

Zhaoran Guo and Shaobo Wang "Implementation of the forward Euler method in MATLAB", Proc. SPIE 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 121632T (22 April 2022); https://doi.org/10.1117/12.2628077

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