Jacobi collocation approximation for solving multi-dimensional Volterra integral equations. (English) Zbl 1401.65148
Summary: This paper addresses the solution of one- and two-dimensional Volterra integral equations (VIEs) by means of the spectral collocation method. The novel technique takes advantage of the properties of shifted Jacobi polynomials and is applied for solving multi-dimensional VIEs. Several numerical examples demonstrate the efficiency of the method and an error analysis verifies the correctness and feasibility of the proposed method when solving VIE.
Keywords:
Volterra integral equation; spectral collocation method; shifted Jacobi polynomials; system of Volterra integral equation; error analysisReferences:
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