Journal of Computational and Applied Mathematics
On spectral methods for Volterra-type integro-differential equations
Journal of Computational and Applied Mathematics
Spectral methods for weakly singular Volterra integral equations with smooth solutions
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Convergence Analysis of Spectral Galerkin Methods for Volterra Type Integral Equations
Journal of Scientific Computing
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The main purpose of this paper is to propose the Legendre spectral-collocation method to solve the Volterra integral equations of the second kind with non-vanishing delay. We divide the definition domain into several subintervals according to the primary discontinuous points associated with the delay. In each subinterval, where the solution is smooth enough, we can apply Legendre spectral-collocation method to approximate the solution. The provided convergence analysis shows that the numerical errors decay exponentially. Numerical examples are presented to confirm this theoretical predict.