An improved algorithm based on Haar scale 3 wavelets for the numerical solution of integro-differential equations

Abstract

The main aim of this research article is to coin a novel numerical algorithm for approximating the solutions of integro-differential equations using Haar scale $3$ wavelets. Highest order derivatives involved in the integro-differential equations are approximated using Haar scale $3$ functions and discretized by collocation technique. The integrals of unknown functions involved in the integro-differential equations are handled by Quadrature formula using Haar scale $3$ wavelets. To explain the supermacy of the proposed algorithm, a few examples from the already published reports have been analyzed. The exact and approximate solutions are compared by calculating the errors at different collocation points. The results are presented through tables and graphs.