Numerical solution of Fredholm and Volterra integral equations using the normalized Müntz−Legendre polynomials
Subject Areas : Numerical Analysis
Fereshteh Saemi
1
,
Hamideh Ebrahimi
2
,
Mahmoud Shafiee
3
1 - Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran,
2 - Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran,
3 - Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran,
Keywords: Operational matrix, Spectral method, Nonlinear Fredholm and Volterra integral equations, Müntz-Legendre polynomials, Stability, error bound, and convergence analysis,
Abstract :
The current research approximates the unknown function based on the normalized Müntz−Legendre polynomials (NMLPs) in conjunction with a spectral method for the solution of nonlinear Fredholm and Volterra integral equations. In this method, by using operational matrices, a system of algebraic equations is derived that can be readily handled through the use of the Newton scheme. The stability, error bound, and convergence analysis of the method are discussed in detail by preparing some theorems. Several illustrative examples are provided formally to show the efficiency of the proposed method.
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