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Convolution Product and Differential and Integro: Differential Equations

In: Analytic Number Theory, Approximation Theory, and Special Functions

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  • Adem Kılıçman

    (University Putra Malaysia, Department of Mathematics and Institute for Mathematical Research)

Abstract

In this paper, we consider partial differential equations with convolution term. Further, by using the convolution we propose a new method to solve the partial differential equations and compare the several properties before and after the convolution. In this new method when the operator has some singularities, then we multiply the partial differential operator with continuously differential functions by using the convolution to remove the singularity. We also study the existence and uniqueness of the new equations. In order to show numerical examples, the following types of problem will be considered: $$\displaystyle{G(x,y) {\ast} P(D)u = f(x,y),}$$ where P(D) is a differential operator. For computational purpose the computer algebra package can be used to solve recurrence relations with associated boundary conditions.

Suggested Citation

  • Adem Kılıçman, 2014. "Convolution Product and Differential and Integro: Differential Equations," Springer Books, in: Gradimir V. Milovanović & Michael Th. Rassias (ed.), Analytic Number Theory, Approximation Theory, and Special Functions, edition 127, pages 737-758, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-0258-3_28
    DOI: 10.1007/978-1-4939-0258-3_28
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