, Volume 40, Issue 1-2, pp 477-497

The spectral method for solving systems of Volterra integral equations

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Abstract

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.