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A New Iteration Method Based on Green’s Functions for the Solution of PDEs

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Abstract

A novel approach that combines iterative methods and Green’s functions is presented for the numerical treatment of a class of partial differential equations (PDEs) subject to specified boundary conditions. The essence of the proposed strategy is to define an integral operator, expressed in terms of Green’s function, and then apply well-known fixed point iterations schemes, including Picard’s and Krasnoselskii–Mann’s. The technique is implemented on a number of examples, including linear and nonlinear PDEs. These numerical experiments elucidate reliability and efficiency of the approach. The results are very promising as they yield highly accurate approximations when compared to closed-form solutions.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, American University of Sharjah, Sharjah, UAE

    S. A. Khuri, A. Sayfy & Aisha Zaveri

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  1. S. A. Khuri
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  2. A. Sayfy
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  3. Aisha Zaveri
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Correspondence to S. A. Khuri.

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Khuri, S.A., Sayfy, A. & Zaveri, A. A New Iteration Method Based on Green’s Functions for the Solution of PDEs. Int. J. Appl. Comput. Math 3, 3091–3103 (2017). https://doi.org/10.1007/s40819-016-0289-x

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