ERROR ESTIMATES OF NONSTANDARD FINITE DIFFERENCE SCHEMES FOR GENERALIZED CAHN-HILLIARD AND KURAMOTO-SIVASHINSKY EQUATIONS

Title & Authors
ERROR ESTIMATES OF NONSTANDARD FINITE DIFFERENCE SCHEMES FOR GENERALIZED CAHN-HILLIARD AND KURAMOTO-SIVASHINSKY EQUATIONS
Choo, Sang-Mok; Chung, Sang-Kwon; Lee, Yoon-Ju;

Abstract
Nonstandard finite difference schemes are considered for a generalization of the Cahn-Hilliard equation with Neumann boundary conditions and the Kuramoto-Sivashinsky equation with periodic boundary conditions, which are of the type $\small{Ut\;+\;\frac{{\partial}^2}{{\partial}x^2} g(u,\;Ux,\;Uxx)\;=\;\frac{{\partial}^{\alpha}}{{\partial}x^{\alpha}}f(U,\;Ux),\;{\alpha}\;=\;0,\;1,\;2}$. Stability and error estimate of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem. Three examples are provided to apply the nonstandard finite difference schemes.
Keywords
nonstandard finite difference scheme;Cahn-Hilliard equation;Kuramoto-Sivashinsky equation;Neumann boundary condition;periodic boundary condition;Lax-Richtmyer equivalence theorem;
Language
English
Cited by
1.
Weak solutions for a class of metaparabolic equations, Applicable Analysis, 2008, 87, 8, 887
2.
Nonstandard finite difference methods: recent trends and further developments, Journal of Difference Equations and Applications, 2016, 22, 6, 817
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