CAS wavelets analytic solution and Genocchi polynomials numerical solutions for the integral and integro-differential equations

Abstract

In this paper, we proposed a new operational matrix of differentiation using CAS wavelets. By aid of these matrices, CAS wavelets method (CASWM) is developed for the Integro-differential equations. Properties of CAS wavelets are used to solve integral and integro-differential equations. Also, we obtain the numerical solutions for Integral equations using Genocchi polynomials with collocation method by reducing a system of algebraic equations. Illustrative numerical problems are considered to demonstrate the applicability of the proposed algorithms such as CASWM yields the exact solution but Genocchi polynomial collocation method (GPCM) yield approximation solution.

Subject Classification:

• 31A10
• 74S30
• 45A05

Keywords:

• CAS wavelets
• Genocchi Polynomials
• Integral and Integro-differential equations
• Collocation method
• Operational matrix