Year: 2008
Communications in Computational Physics, Vol. 4 (2008), Iss. 4 : pp. 820–837
Abstract
We propose a new method for numerical solution of the third-order differential equations. The key idea is to use relaxation approximation to transform the nonlinear third-order differential equation to a semilinear second-order differential system with a source term and a relaxation parameter. The relaxation system has linear characteristic variables and can be numerically solved without relying on Riemann problem solvers or linear iterations. A non-oscillatory finite volume method for the relaxation system is developed. The method is uniformly accurate for all relaxation rates. Numerical results are shown for some nonlinear problems such as the Korteweg-de Vires equation. Our method demonstrated the capability of accurately capturing soliton wave phenomena.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-CiCP-7816
Communications in Computational Physics, Vol. 4 (2008), Iss. 4 : pp. 820–837
Published online: 2008-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18