کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4639727 1341247 2011 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Nonlinear scheme with high accuracy for nonlinear coupled parabolic–hyperbolic system
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Nonlinear scheme with high accuracy for nonlinear coupled parabolic–hyperbolic system
چکیده انگلیسی

A nonlinear finite difference scheme with high accuracy is studied for a class of two-dimensional nonlinear coupled parabolic–hyperbolic system. Rigorous theoretical analysis is made for the stability and convergence properties of the scheme, which shows it is unconditionally stable and convergent with second order rate for both spatial and temporal variables. In the argument of theoretical results, difficulties arising from the nonlinearity and coupling between parabolic and hyperbolic equations are overcome, by an ingenious use of the method of energy estimation and inductive hypothesis reasoning. The reasoning method here differs from those used for linear implicit schemes, and can be widely applied to the studies of stability and convergence for a variety of nonlinear schemes for nonlinear PDE problems. Numerical tests verify the results of the theoretical analysis. Particularly it is shown that the scheme is more accurate and faster than a previous two-level nonlinear scheme with first order temporal accuracy.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 235, Issue 12, 15 April 2011, Pages 3527–3540
نویسندگان
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