A numerical solution to Klein–Gordon equation with Dirichlet boundary condition
khalifa, mohamed essam; Mahmoud Elgamal;
Abstract
Klein–Gordon equation arises in relativistic quantum mechanics and field theory, so it
is of a great importance for the high energy physicists. In this paper, we establish the
existence and uniqueness of the solution and in the second part a numerical scheme is
developed based on finite element method. For one space dimensional case, a complete
numerical algorithm for the numerical solutions using the quadratic interpolation
functions is constructed. The one-dimensional model equation is formulated over an
arbitrary element, applying the assembly process on the elements of the domain,
employing numerical scheme to integrate the nonlinear terms and solving the system of
equations numerically. Finally the obtained results of simulation is visualized, which
shows the overflow of the solution as expected.
2003 Elsevier Inc. All rights reserved.
is of a great importance for the high energy physicists. In this paper, we establish the
existence and uniqueness of the solution and in the second part a numerical scheme is
developed based on finite element method. For one space dimensional case, a complete
numerical algorithm for the numerical solutions using the quadratic interpolation
functions is constructed. The one-dimensional model equation is formulated over an
arbitrary element, applying the assembly process on the elements of the domain,
employing numerical scheme to integrate the nonlinear terms and solving the system of
equations numerically. Finally the obtained results of simulation is visualized, which
shows the overflow of the solution as expected.
2003 Elsevier Inc. All rights reserved.
Other data
Title | A numerical solution to Klein–Gordon equation with Dirichlet boundary condition | Authors | khalifa, mohamed essam ; Mahmoud Elgamal | Keywords | Klein–Gordon wave equation;Existence and uniqueness;Finite element method;Gauss– Legendre quadrature;Runge–Kutta | Issue Date | 2005 | Publisher | ELSEVIER | Journal | Applied Mathematics and Computation | Volume | 160 | Start page | 451 | End page | 475 | DOI | 10.1016/j.amc.2003.11.014 |
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