Solution of Boundary-Value Problems for Integrodifferential Equations Via Higher-Order Haar Wavelet Method

Abstract

Abstract. This study presents the approximate solution of boundary-value problems (BVPs) of integrodifferential equations (IDEs) using the higher-order Haar wavelet method (HOHWM). HOHWM is an improvement of the most popular Haar wavelet method and depends on a parameter λ. The method is applied to both Volterra and Fredholm types of IDEs having Dirichlet boundary conditions (BCs). The advantages of this method include higher accuracy, ease of implementation, and good computing efficiency. The method is applied to several problems available in the literature. In the case of HOHWM, second- and fourth-order convergence are observed, which is an improvement over the first-order convergence of the Haar wavelet method (HWM). The obtained results for values of λ=1 and λ=2, respectively, using this method are illustrated by some numerical examples at the end of this paper.