Article

Journal of Engineering Mathematics

, Volume 29, Issue 4, pp 347-369

First online:

Numerical solutions of a damped Sine-Gordon equation in two space variables

  • K. DjidjeliAffiliated withDepartment of Ship Science, University of Southampton
  • , W. G. PriceAffiliated withDepartment of Ship Science, University of Southampton
  • , E. H. TwizellAffiliated withDepartment of Ship Science, University of Southampton Email author 

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Abstract

Numerical solutions of the perturbed Sine-Gordon equation in two space variables, arising from a Josephson junction are presented. The method proposed arises from a two-step, one parameter method for the numerical solution of second-order ordinary differential equations. Though implicit in nature, the method is applied explicitly. Global extrapolation in both space and time is used to improve the accuracy. The method is analysed with respect to stability criteria and numerical dispersion. Numerical results are obtained for various cases involving line and ring solitons.