Abstract
The purpose of this paper was to propose a new method to solve partial differential equations arising in the field of science and engineering. In this new method, we have reduced the multiple integrals into a single integral and expressed it in terms of a difference kernel. To make the calculation easy and convenient, we have used the Laplace transformation to solve the difference kernel. The method is very simple, easy to understand and calculation minimizing as compared to the Adomian decomposition method and the variational iteration method. Some examples are given to verify the reliability and efficiency of the method.
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Acknowledgments
The first author acknowledges the support of Hafr Al-Batin University, Saudi Arabia, and third author was realized in CEITEC—Central European Institute of Technology with research infrastructure supported by the project CZ.1.05/1.1.00/02.0068 financed from European Regional Development Fund and by the project FEKT-S-14-2200 of Faculty of Electrical Engineering and Communication, Brno University of Technology.
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Khan, Y., Faraz, N. & Smarda, Z. Difference kernel iterative method for linear and nonlinear partial differential equations. Neural Comput & Applic 27, 671–675 (2016). https://doi.org/10.1007/s00521-015-1886-z
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DOI: https://doi.org/10.1007/s00521-015-1886-z