Legendre Wavelet Collocation Solution for System of Linear and Nonlinear Delay Differential Equations

Abstract

The proposed article is to describe the study of the system of linear and nonlinear delay differential equations subjected to initial-interval conditions. The existence and uniqueness theorem for solution of the proposed problem has been provided. The Legendre wavelet collocation method has been used in solution. We are presenting certain powerful tools as wavelet concepts, properties and description of this method. The main objective of the proposed method is to achieve high accuracy in minimum computation. The convergence analysis of Legendre wavelet collocation method is also presented. Some numerical examples of linear and non-linear system of delay differential equations are discussed in detail. The comparative study of Legendre wavelet collocation method, Exact, Runge–Kutta fourth order, dde23 (MATLAB solver) and Taylor’s series method solutions are also provided.