An efficient spectral method for solving third-kind Volterra integral equations with non-smooth solutions

2022/07/15 by Younes Talaei, Talaei, Younes, Pedro M. Lima +1
Mathematics · #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2207.07405

openalex publication_date 2022/07/15 · openalex created_date 2022/07/19 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the numerical solution of the third kind Volterra integral equations with non-smooth solutions based on the recursive approach of the spectral Tau method. To this end, a new set of the fractional version of canonical basis polynomials (called FC-polynomials) is introduced. The approximate polynomial solution (called Tau-solution) is expressed in terms of FC-polynomials. The fractional structure of Tau-solution allows recovering the standard degree of accuracy of spectral methods even in the case of non-smooth solutions. The convergence analysis of the method is studied. The obtained numerical results show the accuracy and efficiency of the method compared to other existing methods.

Related

• A new recursive spectral Tau method on system of generalized Abel-Volterra integral equations
• A Method for Numerical Solution of Third-Kind Volterra Integral Equations Using Krall-Laguerre Polynomials
• On the Approximate Solution of Integral Equations with Logarithmic Kernels Using the Third Kind of Chebyshev Polynomials
• Numerical Study of Index-v First kind Volterra Integral Equations as Ill-posed Problem
• Shifted Chebyshev polynomials for Solving Three-Dimensional Volterra Integral Equations of the second kind