Efficient high-order finite difference methods for nonlinear Klein–Gordon equations. I: Variants of the phi-four model and the form-I of the nonlinear Klein–Gordon equation
Articles
Ascensión Hernández Hernández Encinas
University of Salamanca, Spain
Jesus Martín-Vaquero
University of Salamanca, Spain
Araceli Queiruga-Dios
University of Salamanca, Spain
Víctor Gayoso-Martínez
Spanish National Research Council (CSIC), Spain
Published 2015-04-20
https://doi.org/10.15388/NA.2015.2.9
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Keywords

Klein–Gordon equations
finite difference methods
numerical methods
phi-four model

How to Cite

Encinas, A.H.H. (2015) “Efficient high-order finite difference methods for nonlinear Klein–Gordon equations. I: Variants of the phi-four model and the form-I of the nonlinear Klein–Gordon equation”, Nonlinear Analysis: Modelling and Control, 20(2), pp. 274–290. doi:10.15388/NA.2015.2.9.

Abstract

In this paper, the problem of solving some nonlinear Klein–Gordon equations (KGEs) is considered. Here, we derive different fourth- and sixth-order explicit and implicit algorithms to solve the phi-four equation and the form-I of the nonlinear Klein–Gordon equation. Stability and consistency of the proposed schemes are studied under certain conditions. Numerical results are presented and then compared with others obtained from some methods already existing in the scientific literature to explain the efficiency of the new algorithms. It is also shown that similar schemes can be proposed to solve many classes of nonlinear KGEs.

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