A spectral element solution of the Klein–Gordon equation with high-order treatment of time and non-reflecting boundary
نویسندگان
چکیده
A spectral element (SE) implementation of the Givoli–Neta non-reflecting boundary condition (NRBC) is considered for the solution of the Klein–Gordon equation. The infinite domain is truncated via an artificial boundary B, and a high-order NRBC is applied on B. Numerical examples, in various configurations, concerning the propagation of a pressure pulse are used to demonstrate the performance of the SE implementation. Effects of time integration techniques and long term results are discussed. Specifically, we show that in order to achieve the full benefits of high-order accuracy requires balancing all errors involved; this includes the order of accuracy of the spatial discretization method, timeintegrators, and boundary conditions. Published by Elsevier B.V.
منابع مشابه
Analytical solutions for the fractional Klein-Gordon equation
In this paper, we solve a inhomogeneous fractional Klein-Gordon equation by the method of separating variables. We apply the method for three boundary conditions, contain Dirichlet, Neumann, and Robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.
متن کاملApplications of He’s Variational Principle method and the Kudryashov method to nonlinear time-fractional differential equations
In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...
متن کاملB-SPLINE COLLOCATION APPROACH FOR SOLUTION OF KLEIN-GORDON EQUATION
We develope a numerical method based on B-spline collocation method to solve linear Klein-Gordon equation. The proposed scheme is unconditionally stable. The results of numerical experiments have been compared with the exact solution to show the efficiency of the method computationally. Easy and economical implementation is the strength of this approach.
متن کاملNumerical solution of Klein-Gordon equation by using the Adomian's decomposition and variational iterative methods
متن کامل
SOLVING NONLINEAR KLEIN-GORDON EQUATION WITH A QUADRATIC NONLINEAR TERM USING HOMOTOPY ANALYSIS METHOD
In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM).Comparisons are made between the Adomian decomposition method (ADM), the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple.
متن کامل