Premium
A semi‐adaptive split‐cosine scheme for the sine‐Gordon equation
Author(s) -
Sheng Q.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700806
Subject(s) - sine gordon equation , nonlinear system , mathematics , ordinary differential equation , sine , mathematical analysis , scheme (mathematics) , stability (learning theory) , trigonometric functions , sine wave , differential equation , physics , soliton , computer science , geometry , quantum mechanics , machine learning , voltage
This talk concerns the numerical solution of the nonlinear sine‐Gordon equation in rectangular large‐area Josephson junctions. An application of the adaptive method of lines leads to a system of second‐order nonlinear ordinary differential equations. The system is approximated by a nonlinear recurrence relation. Strang's splitting is then introduced for establishing a highly effective and stable semi‐adaptive scheme. The novel new method offers an efficient way in the solitary wave solution approximations. A stability analysis is presented. Straightforward numerical demonstrations on ring solitons up to higher time levels are given. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)