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

In: Contributions in Mathematics and Engineering

Author

Listed:
  • I. N. Parasidis

    (TEI of Thessaly, Department of Electrical Engineering)

  • E. Providas

    (TEI of Thessaly, Department of Mechanical Engineering)

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.

Suggested Citation

  • I. N. Parasidis & E. Providas, 2016. "Extension Operator Method for the Exact Solution of Integro-Differential Equations," Springer Books, in: Panos M. Pardalos & Themistocles M. Rassias (ed.), Contributions in Mathematics and Engineering, pages 473-496, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-31317-7_23
    DOI: 10.1007/978-3-319-31317-7_23
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