본문 바로가기
KERD
논문KCI 등재

Error estimates of nonstandard finite difference schemes for generalized Cahn-Hilliard and Kuramoto-Sivashinsky equations

이윤주|정상권|추상목
대한수학회 (The Korean Mathematical Society)|2005.11|대한수학회지 (Journal of the KMS)|제42권 제6호|pp. 1121-1136

1

조회

0

다운로드

3

인용

0

참고문헌

주제분류수학

초록

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 $$u_t+\frac{\partial^2}{\partial x^2}g(u,u_x,u_{xx}) =\frac{\partial^\alpha}{\partial x^\alpha} f(u, u_x),\,\alpha=0,1,2.$$ 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.

참고문헌 (14)

  1. "Monographs andTextbooks in Pure and Applied Mathematics", 155 (1992), Marcel Dekker Inc.
  2. "Finite difference discretization of the", (1), pp.1~ (1992)
  3. "Finite element discretization of the", 29, pp.155~163 (1994), Banach CenterPubl.
  4. "Conservative nonlinear differencescheme for the {Cahn-{H}illiard equation", 36(7), pp.31~39 (1998)
  5. "Conservativenonlinear differencescheme for the", 39(1-2), pp.229~243 (2000)
  6. "A Conservativedifferencescheme for the viscous H}illiard equation with a nonconstant gradient energy coefficient}", 51(2--3), pp.207~219 (2004)
  7. "Numerical studies of the H}illiard equation for phase separation}", (2), pp.97~ (1987)
  8. "A nonconforming finite-element method for thetwo-dimensional", (4), pp.884~ (1989)
  9. "A stable and conservative finite differencescheme forthe {Cahn-{H}illiard equation", 87(4), pp.675~699 (2001)
  10. "L}inear investigation of nonlinear stability}", (1), pp.71~ (1988)
  11. "Second-ordersplittingcombined with orthogonal cubic spline collocation method for the", 35(6), pp.5~25 (1998)
  12. "Applications of nonstandard finite differenceschemes" (2000), World Scientific
  13. "Nonlinear stability andconvergence offinite-difference methods for the ``good''", (2), pp.215~58 (1990)
  14. "The well-posedness of the", (4), pp.884~ (1986)

관련 논문AI추천

A fourth-order accurate finite difference scheme for the extended-Fisher-Kolmogorov equationKhaled Omrani, Tlili Kadri대한수학회 · 대한수학회보2018 · 제55권 제1호SPECTRAL APPROXIMATIONS OF ATTRACTORS FOR CONVECTIVE CAHN-HILLIARD EQUATION IN TWO DIMENSIONSXiaopeng Zhao대한수학회 · 대한수학회보2015 · 제52권 제5호A hybrid method for higher-order nonlinear diffusion equations김준석, Jeanman Sur대한수학회 · 대한수학회논문집2005 · 제20권 제1호L^2-error analysis of fully discrete discontinuous Galerkin approximations for nonlinear Sobolev equations엄미례, 이현영대한수학회 · 대한수학회보2011 · 제48권 제5호An Extrapolated Higher Order Characteristic Finite Element Method for Nonlinear Sobolev Equations신준용, 엄미례영남수학회 · East Asian Mathematical Journal2018 · 제34권 제5호Error estimates for fully discrete mixed discontinuous Galerkin approximations for parabolic problems신준용, 엄미례, 이현영영남수학회 · East Asian Mathematical Journal2015 · 제31권 제5호

이 간행물의 다른 논문 (13건)

Spectral dualities of $MV$-algebrasYoung Soo Park, Eun Sup Kim, Tae Ho Choepp. 1111-1120Global Existence and Stability for Euler-Bernoulli Beam Equation with memory condition at the boundary김정애, 박종열pp. 1137-1152$R$-homomorphisms and $R$-homogeneous maps조용욱pp. 1153-1167The properties of the transversal Killing spinor and transversal twistor spinor for Riemannian foliations정승달, 문영봉pp. 1169-1186Asymptotic number of General Cubic Graphs with given Connectivity채갑병pp. 1187-1203
원문 보기