Study on convergence of hybrid functions method for solution of nonlinear integral equations

Abstract

In this article, we present the uniform convergence analysis and accuracy estimation of hybrid functions (HFs) method for finding the solution of nonlinear Volterra and Fredholm integral equations. The properties of HFs which consist of block-pulse functions (BPFs) and Legendre polynomials are used to reduce the solution of nonlinear integral equations to the solution of algebraic equations. The superiority and accuracy of the HFs method to BPF and Legendre polynomial methods are illustrated through some numerical examples.

Keywords:

• nonlinear integral equation
• hybrid functions
• block-pulse functions
• Legendre polynomials
• convergence analysis

AMS Subject Classifications::

• 65R20
• 65L20