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Galerkin-FEM for obtaining the numerical solution of the linear fractional Klein-Gordon equation
Khadijah Mohammed,Meabed Khedr
Keywords:Fractional Klein-Gordon equation; Galerkin finite element method; Quadrati B-spline functions; Stability analysis
Abstract:
      In this article, 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 replacement the Caputo fractional derivative using $L2$ discretization formula. The proposed method reduces LFKGE to a system of algebraic equations, which solved using conjugate gradient method. Special attention is given to study the stability analysis to the approximation obtained by the proposed scheme. 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.