On the numerical solution of the Klein‐Gordon equation
Copyright policy )On the numerical solution of the Klein‐Gordon equation
AbstractA predictor–corrector (P–C) scheme based on the use of rational approximants of second‐order to the matrix‐exponential term in a three‐time level reccurence relation is applied to the nonlinear Klein‐Gordon equation. This scheme is accelerated by using a modification (MPC) in which the already evaluated values are used for the corrector. Both the predictor and the corrector scheme are analyzed for local truncation error and stability. The proposed method is applied to problems possessing periodic, kinks and single, double‐soliton waves. The accuracy as well as the long time behavior of the proposed scheme is discussed. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009
- University of West Attica Greece
Method of lines for initial value and initial-boundary value problems involving PDEs, Finite difference and finite volume methods for ordinary differential equations, Soliton equations, predictor-corrector, finite-difference method, method of lines, error bounds, stability, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Error bounds for initial value and initial-boundary value problems involving PDEs, KdV equations (Korteweg-de Vries equations), Klein-Gordon equation, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, soliton
Method of lines for initial value and initial-boundary value problems involving PDEs, Finite difference and finite volume methods for ordinary differential equations, Soliton equations, predictor-corrector, finite-difference method, method of lines, error bounds, stability, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Error bounds for initial value and initial-boundary value problems involving PDEs, KdV equations (Korteweg-de Vries equations), Klein-Gordon equation, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, soliton
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