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The spectral method for solving systems of Volterra integral equations. (English) Zbl 1295.65128
Summary: This paper presents a high accurate and stable Legendre-collocation method for solving systems of Volterra integral equations (SVIEs) of the second kind. The method transforms the linear SVIEs into the associated matrix equation. In the nonlinear case, after applying our method we solve a system of nonlinear algebraic equations. Also, sufficient conditions for the existence and uniqueness of the linear SVIEs, in which the coefficient of the main term is a singular (or nonsingular) matrix, have been formulated. Several examples are included to illustrate the efficiency and accuracy of the proposed technique and also the results are compared with the different methods. All of the numerical computations have been performed on a PC using several programs written in MAPLE 13.

65R20 Numerical methods for integral equations
45F05 Systems of nonsingular linear integral equations
45G15 Systems of nonlinear integral equations
45D05 Volterra integral equations
Full Text: DOI
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