2019 Volume 9 Issue 1

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M. M. Khader, Khadijah M. Abualnaja. GALERKIN-FEM FOR OBTAINING THE NUMERICAL SOLUTION OF THE LINEAR FRACTIONAL KLEIN-GORDON EQUATION[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 261-270. doi: 10.11948/2019.261

Citation:

M. M. Khader, Khadijah M. Abualnaja. GALERKIN-FEM FOR OBTAINING THE NUMERICAL SOLUTION OF THE LINEAR FRACTIONAL KLEIN-GORDON EQUATION[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 261-270. doi: 10.11948/2019.261

GALERKIN-FEM FOR OBTAINING THE NUMERICAL SOLUTION OF THE LINEAR FRACTIONAL KLEIN-GORDON EQUATION

M. M. Khader^1,2, ,,
Khadijah M. Abualnaja³

1.
Department of Mathematics and Statistics, College of Science, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia
2.
Department of Mathematics, College of Science, Benha University, Benha, Egypt
3.
Department of Mathematics and Statistics, College of Science, Taif University, Taif, KSA

Corresponding author: Email address:mohamedmbd@yahoo.com(M. M. Khader)

Abstract

Abstract

In this paper, an efficient numerical method for solving the linear fractional Klein-Gordon equation (LFKGE) is introduced. The proposed method depends on the Galerkin finite element method (GFEM) using quadratic B-spline base functions and replaces the Caputo fractional derivative using $ L2 $ discretization formula. The introduced technique reduces LFKGE to a system of algebraic equations, which solved using conjugate gradient method. The study the stability analysis to the approximation obtained by the proposed scheme is given. To test the accuracy of the proposed method we evaluated the error norm $ L_{2} $. It is shown that the presented scheme is unconditionally stable. Numerical example is given to show the validity and the accuracy of the introduced algorithm.
- Fractional Klein-Gordon equation /
- Galerkin finite element method /
- quadratic B-spline functions /
- stability analysis
MSC: 41A30, 41A55, 65N12, 65N30

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References

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