Numerical solution of fractional diffusion wave equation and fractional Klein–Gordon equation via two-dimensional Genocchi polynomials with a Ritz–Galerkin method

Kanwal, Afshan and Phang, Chang and Iqbal, Umer (2018) Numerical solution of fractional diffusion wave equation and fractional Klein–Gordon equation via two-dimensional Genocchi polynomials with a Ritz–Galerkin method. Computation, 6 (3). ISSN 20793197

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Official URL: doi:10.3390/computation6030040

Abstract

In this paper, two-dimensional Genocchi polynomials and the Ritz–Galerkin method were developed to investigate the Fractional DiffusionWave 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.

Item Type:Article
Uncontrolled Keywords:Genocchi polynomials; Ritz–Galerkin method; time-fractional diffusion wave equation; time-fractional nonlinear Klein–Gordon equation; fractional partial differential equations
Subjects:Q Science > QA Mathematics > QA297 Numerical analysis. Analysis
Divisions:Faculty of Applied Science and Technology > Department of Mathematics and Statistic
ID Code:11195
Deposited By:Mr. Mohammad Shaifulrip Ithnin
Deposited On:13 May 2019 09:13
Last Modified:13 May 2019 09:13

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