Legendre wavelet solution of high order nonlinear ordinary delay differential equations

Abstract

The purpose of this paper is to illustrate the use of the Legendre wavelet method in the solution of high-ordernonlinear ordinary differential equations with variable and proportional delays. The main advantage of using Legendrepolynomials lies in the orthonormality property, which enables a decrease in the computational cost and runtime. Themethod is applied to five differential equations up to sixth order, and the results are compared with the exact solutionsand other numerical solutions when available. The accuracy of the method is presented in terms of absolute errors. Thenumerical results demonstrate that the method is accurate, effectual and simple to apply