2020/06/09 by Fereshteh Saemi, Saemi, Fereshteh, Hamideh Ebrahimi +3
Mathematics · #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Müntz-Legendre polynomials #Nonlinear Fredholm and Volterra integral equations #Operational matrix #Spectral method #Stability #and convergence analysis #error bound
paper · doi:10.82521/ijo.2022.1018852
openalex publication_date 2020/06/09 · openalex created_date 2021/03/29 · openalex updated_date 2026/07/07
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.