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In this paper, a nonclassical sinc collocation method is constructed to the numerical solution of systems of second-order integro-differential equations of Volterra and Fredholm types. The novelty of the approach is based on using the new non classical weight function for sinc method instead of the classic ones. The sinc collocation method based on non classical weight functions is used to reduce the system of integro-differential equations to a system of algebraic equations which can be solved numerically. Furthermore, the convergence of the method is proposed theoretically which shows that the method converges exponentially. By solving some examples numerically, the results are compared with other methods to demonstrate the efficiency of the new method.

In this paper, a nonclassical sinc collocation method is constructed for the numerical solution of systems of second-order integro-differential equations of the Volterra and Fredholm types. The novelty of the approach is based on using the new nonclassical weight function for sinc method instead of the classic ones. The sinc collocation method based on nonclassical weight functions is used to reduce the system of integro-differential equations to a system of algebraic equations. Furthermore, the convergence of the method is proposed theoretically, showing that the method converges exponentially. By solving some examples, including problems with a non-smooth solution, the results are compared with other existing results to demonstrate the efficiency of the new method.

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