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Computation 2018, 6(3), 40; https://doi.org/10.3390/computation6030040

Numerical Solution of Fractional Diffusion Wave Equation and Fractional Klein–Gordon Equation via Two-Dimensional Genocchi Polynomials with a Ritz–Galerkin Method

1
Department of Mathematics and Statistics, Universiti Tun Hussein Onn Malaysia, Pagoh Campus, 84600 Pagoh, Malaysia
2
Riphah College of Computing, Riphah International University, Faisalabad Campus, 38000 Faisalabad, Pakistan
*
Author to whom correspondence should be addressed.
Received: 31 May 2018 / Revised: 21 June 2018 / Accepted: 25 June 2018 / Published: 27 June 2018
(This article belongs to the Section Computational Engineering)
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Abstract

In this paper, two-dimensional Genocchi polynomials and the Ritz–Galerkin method were developed to investigate the Fractional Diffusion Wave Equation (FDWE) and the Fractional Klein–Gordon Equation (FKGE). A satisfier function that satisfies all the initial and boundary conditions was used. A linear system of algebraic equations was obtained for the considered equation with the help of two-dimensional Genocchi polynomials along with the Ritz–Galerkin method. The FDWE and FKGE, including the nonlinear case, were reduced to solve the linear system of the algebraic equation. Hence, the proposed method was able to greatly reduce the complexity of the problems and provide an accurate solution. The effectiveness of the proposed technique is demonstrated through several examples. View Full-Text
Keywords: Genocchi polynomials; Ritz–Galerkin method; time-fractional diffusion wave equation; time-fractional nonlinear Klein–Gordon equation; fractional partial differential equations Genocchi polynomials; Ritz–Galerkin method; time-fractional diffusion wave equation; time-fractional nonlinear Klein–Gordon equation; fractional partial differential equations
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Kanwal, A.; Phang, C.; Iqbal, U. Numerical Solution of Fractional Diffusion Wave Equation and Fractional Klein–Gordon Equation via Two-Dimensional Genocchi Polynomials with a Ritz–Galerkin Method. Computation 2018, 6, 40.

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