Journal
NUMERICAL ALGORITHMS
Volume 52, Issue 4, Pages 523-540Publisher
SPRINGER
DOI: 10.1007/s11075-009-9296-x
Keywords
Klein-Gordon (KG) equation; Compact finite difference; Diagonally-implicit Runge-Kutta-Nystrom (DIRKN) methods; High accuracy; Soliton
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In this work we propose a fourth-order compact method for solving the one-dimensional nonlinear Klein-Gordon equation. We apply a compact finite difference approximation of fourth-order for discretizing spatial derivative and a fourth-order A-stable diagonally-implicit Runge-Kutta-Nystrom (DIRKN) method for the time integration of the resulting nonlinear second-order system of ordinary differential equations. The proposed method has fourth order accuracy in both space and time variables and is unconditionally stable. Numerical results obtained from solving several problems possessing periodic, kinks, single and double-soliton waves show that the combination of a compact finite difference approximation of fourth order and a fourth-order A-stable DIRKN method gives an efficient algorithm for solving these problems.
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