Integro-differential equations: Numerical solution by a new operational matrix based on fourth-order hat functions

Abstract

This article aims to present a new approach based on the operational matrix method for solving integro-differential equations using numerical techniques. In this method, we employ fourth-degree hat functions (FDHFs) to construct operational matrices. The approach involves two main steps. First, we utilize FDHFs to create operational matrices, which allows us to transform the given problem into a system of algebraic equations. The second step involves solving these algebraic equations numerically. Additionally, we provide an analysis of the errors involved and compare the proposed method with existing techniques. The results demonstrate that the proposed method outperforms its counterparts, highlighting its superiority.

Keywords

• Fourth-degree hat functions
• Nonlinear Volterra integro-differential equations
• Operational matrix
• Error analysis