Extension Operator Method for the Exact Solution of Integro-Differential Equations

I. N. Parasidis () and E. Providas ()
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I. N. Parasidis: TEI of Thessaly, Department of Electrical Engineering
E. Providas: TEI of Thessaly, Department of Mechanical Engineering

A chapter in Contributions in Mathematics and Engineering, 2016, pp 473-496 from Springer

Abstract: Abstract An exact method for the solution of the linear Fredholm integro-differential equations is proposed. The method is based on the correct extensions of minimal operators in Banach spaces. The integro-differential operator B is formulated as an extension of a minimal operator A 0 and as a perturbation of a correct differential operator $$\widehat{A}$$ . If the operator B is correct, then the unique solution of the integro-differential equation is obtained in closed form. The method can be easily programmed in a computer algebra system. Since there are not any general exact methods for solving integro-differential equations, the present approach can form the base for further study in this direction.

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-31317-7_23

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DOI: 10.1007/978-3-319-31317-7_23

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