Numerical solution of nonlinear weakly singular Volterra integral equations of the first kind: An hp-version collocation approach

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 this nonlinear Volterra 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 L-2-norm. The efficiency of the method is illustrated by some numerical experiments. (c) 2020 IMACS. Published by Elsevier B.V. All rights reserved.

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This paper focuses on the numerical solution of a class of nonlinear weakly singular Volterra integral equations of the first kind, introducing an hp-version collocation method with Jacobi polynomials. The efficiency of the method is demonstrated through numerical experiments.