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Two-dimensional integral-algebraic systems: analysis and computational methods

Bulatov, M.V. ; Lima, Pedro M.

Journal of Computational and Applied Mathematics, 236(12) (2011), 132-140

In this article we formulate sufficient conditions for the existence and uniqueness of solution to systems of two-dimensional Volterra integral equations, in which the coefficient of the main term is a singular matrix. A numerical method is introduced which can be applied to approximate the solution when the given conditions are satisfied. The convergence of this method is proved and illustrated by numerical examples.