Numerical Solutions of Ordinary Differential Equations Using Mathematica

Abstract

This paper investigated the numerical solution of linear ordinary differential equations using Mathematica. The computational software (Mathematica) automates tedious numerical computations, making it easier to generate accurate numerical solutions. Several programming paradigm can be used to implement these numerical algorithms (methods) via Mathematica, but this paper briefly featured two of the programming paradigm, the Recursive and Functional paradigm. The software to generate the necessary solution to a given ordinary differential equation, plot its graph and compare the different numerical methods for higher accuracy using the plotted graphs. We compare the NDSolveapproachin Mathematica with that of Euler and Runge-Kutta method. We observe that the NDSolve and Runge-Kutta produces similar results.