On the construction of functional polynomials for solutions of integro-differential equations

The object of research is the integro-differential equations of mathematical physics. The subject of the study is the construction of interpolation polynomials to obtain approximate solutions of such equations. The paper presents a method of constructing approximate expressions for functionals on solutions of integro-differential equations, which are analogous to the Hermite interpolation polynomial used in interpolation of functions. By the example of the diffusion equation it is shown that the use of several basic solutions can significantly improve the accuracy of the approximate representation of functions in comparison with the first approximation of the perturbation theory at almost the same labor costs.

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