Numerical Solution of Nonlinear Abel Integral Equations: An hp -Version Collocation Approach

2020/01/17 by Dehbozorgi, Raziyeh, Khadijeh Nedaiasl, Nedaiasl, Khadijeh
Mathematics · #45D05 #45H30 #65L60 #65L70 #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical functions and polynomials #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2001.06240

openalex publication_date 2020/01/17 · openalex created_date 2020/01/23 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the numerical solution for a class of nonlinear weakly singular Volterra integral equation of the first kind. The existence and uniqueness issue of the nonlinear Abel integral equations is studied completely. An hp-version collocation method in conjunction with Jacobi polynomials is introduced so as an appropriate numerical solution to be found. We analyze it properly and find an error estimation in L²-norm. The efficiency of the method is illustrated by some numerical experiments.

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