Abstract
In this paper, we put forward a new spectral element method for the nonlinear second-kind Volterra integral equations (VIEs) with weakly singular kernel, which employs shifted Müntz–Jacobi functions and shifted Legendre polynomials as basis functions. This method is capable of approximating the limited regular solution more efficiently. We analyze the existence and uniqueness of the solution to the numerical scheme and derive the hp-version optimal convergence under some reasonable assumptions. A series of numerical examples are presented to demonstrate the efficiency of the new method.
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