# Numerical Solution of Nonlinear Abel Integral Equations: 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 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 L^2-norm. The efficiency of the method is illustrated by some numerical experiments.

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