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A sixth‐order compact finite difference method for the one‐dimensional sine‐Gordon equation
Author(s) -
Sari Murat,
Gürarslan Gürhan
Publication year - 2011
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1349
Subject(s) - scheme (mathematics) , compact finite difference , mathematics , sine gordon equation , space (punctuation) , order (exchange) , stability (learning theory) , sine , finite difference , finite difference scheme , finite difference method , order of accuracy , finite difference coefficient , numerical analysis , mathematical analysis , numerical stability , computer science , finite element method , engineering , geometry , physics , mixed finite element method , structural engineering , operating system , quantum mechanics , machine learning , soliton , finance , nonlinear system , economics
This paper explores the utility of a sixth‐order compact finite difference (CFD6) scheme for the solution of the sine‐Gordon equation. The CFD6 scheme in space and a third‐order strong stability preserving Runge–Kutta scheme in time have been combined for solving the equation. This scheme needs less storage space, as opposed to the conventional numerical methods, and causes to less accumulation of numerical errors. The scheme is implemented to solve three test problems having exact solutions. Comparisons of the computed results with exact solutions showed that the method is capable of achieving high accuracy with minimal computational effort. The present results are also seen to be more accurate than some available results given in the literature. The scheme is seen to be a very reliable alternative technique to existing ones. Copyright © 2009 John Wiley & Sons, Ltd.