Numerical method for solving arbitrary linear differential equations using a set of orthogonal basis functions and operational matrix

Abstract

This article presents a numerical method for solving ordinary linear differential equations of arbitrary order and coefficients. For this purpose, block-pulse functions (BPFs) as a set of piecewise constant orthogonal functions are used. By the BPFs vector forms and operational matrix of integration, solving the differential equation is reduced to solve a linear system of algebraic equations. Some problems are numerically solved by the proposed method to illustrate its generality and computational efficiency for solving an arbitrary linear differential equation. For further evaluation, mean-absolute errors and running times associated with the method are given to show that the method is convergent and runs in a reasonable time.