Abstract
This paper presents a numerical algorithm for solving linear delay Volterra integral equations with a spatial variable. The theory on compact operators is utilized to prove the existence and uniqueness of solution for the original equation, by combining the trapezoidal quadrature formula with interpolation to obtain an approximate equation. Then, we validate the existence of the approximate solution by analyzing the convergence of iterative sequence. The uniqueness of the approximate solution is proved by applying a two-dimensional discrete Gronwall inequality. Next, the convergence of the approximate solution and the asymptotic expansion of errors are obtained. Moreover, a higher accuracy solution is obtained by means of splitting extrapolation algorithms. Some numerical experiments are provided to demonstrate the efficiency of the proposed method.
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