Abstract
The nonlinear parabolic equations in a variable domain are considered. A modified upwind difference scheme is given in the variable domain. Stability in l-norm and error estimate in I 2-norm are obtained.
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Axelsson, O. and Gustafasson, I.. A modified upwind scheme for convective transport equations and the use of a conjugate gradient method for the solution of non-symmetric systems of equations. J. Imt. Maths. Applies., 23(1979), 321–337.
Ewing. R. E. ⋅ Lazarov. R. D. and Vassilev, A. T., Finite difference scheme for parabolic problems on composite grids with refinement in time and space, SI AM J. Numer. Anal., 31(1994), 1605–1622.
Gao Zhiming, On the convergence of difference schemes for nonlinear heat conduction equation with moving boundary condition, Math. Numer. Sinica (Chinese), 4(1982), 139–150.
Yuan Yirang, Characteristic finite difference methods for moving boundary value problem of numerical simulation of oil deposit, Science in China. 37(1994), 1442–1453.
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The project supported by the National Natural Science Foundation of China.
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Mingrong, C. A modified upwind difference scheme for nonlinear parabolic equations in a variable domain. Appl. Math. Chin. Univ. 12, 411–418 (1997). https://doi.org/10.1007/s11766-997-0043-6
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DOI: https://doi.org/10.1007/s11766-997-0043-6