A Hybrid Numerical Approach for Volterra Integro-Differential Equations via Block-Pulse and Muntz Functions

In this paper, we present a novel set of hybrid functions using the Block-Pulse functions and a new class of Muntz functions to obtain numerical solutions for Volterra integro-differential equations (VIDEs). In this method, by implementing the collocation approach based on the new hybrid basis as the trial functions, the given VIDE is reformulated as a system of algebraic equations. As opposed to the existing methods that use M¨untz–Legendre polynomials, we utilize a new set of M¨untz functions that have distinct real roots in the interval [0, 1]. Furthermore, the convergence, stability and accuracy of the method are studied. Numerical examples are included to demonstrate the efficiency and high accuracy of the proposed approach.