Abstract:

In this study, we suggested a novel approach for solving multi-functional integro-differential equations with mixed delays, by using orthogonal Jacobi polynomials. These equations include various classes of differential equations, integro-differential equations and delay differential equations. This new algorithm proposes solutions for each class of these equations and combinations of equation classes, such as Volterra integro-differential equation, Fredholm integro-differential equation, pantograph-delay differential equations. Since the present method is based on fundamental matrix relations and collocation points, numerical solutions can be obtained easily by means of symbolic computation programs. We developed an error estimation algorithm based on the present method for the verification of solutions. Application of the method is illustrated by four numerical examples.

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