Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials

Abstract EN

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented.

This method is based upon hybrid functions approximation.

The properties of hybrid functions consisting of block-pulsefunctions and Bernoulli polynomials are presented.

The operational matrices ofintegration and product are given.

These matrices are then utilized to reducethe nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraicequations.

Illustrative examples are included to demonstrate the validityand applicability of the technique.