Numerical Solution of Two-Dimensional Fractional Order Diffusion Equation by using Elzaki Transform with Residual Power Series Method

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Published: Sep 15, 2023
Keywords:
Elzaki transforms, fractional order diffusion equation, residual power series method, inverse Elzaki transform

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Geeta Arora
Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Punjab, India
Rajendra Pant
Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Punjab, India

Abstract

The Elzaki transform with RPS method is an efficient and reliable approach for solution of non-integer order linear as well as non-linear differential equations. The major endeavour of current work is to find the solution of two dimensional non-integer order diffusion equation by Elzaki transform with RPS method. Firstly, Elzaki is applied on this equation. Secondly, inverse Elzaki is taken on this equation for finding the expression of solution. Thirdly, assumed approximate solution is substituted on this equation. Then unidentified coefficient functions are obtained by using residual function is equal to zero as well as combining its initial circumstances. At last, coefficient functions are substituted in power series form for finding finite approximate logical solutions. The judgment between exact solution and approximate analytic solutions with different number of terms of this equation are determined and compared for reliability. This method reduces the size of computational works of solution of non-integer order non-linear diffusion equation.

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Arora G, Pant R. Numerical Solution of Two-Dimensional Fractional Order Diffusion Equation by using Elzaki Transform with Residual Power Series Method. J. Int. Acad. Phys. Sci. [Internet]. 2023 Sep. 15 [cited 2024 May 18];27(3):225-3. Available from: https://www.iaps.org.in/journal/index.php/journaliaps/article/view/891
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Vol. 27 No. 3 (2023): Table of Content
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