Nonlinear scheme with high accuracy for nonlinear coupled parabolic-hyperbolic system

作者：Cui Xia; Yue Jing yan^*; Yuan Guang wei

来源：Journal of Computational and Applied Mathematics, 2011, 235(12): 3527-3540.

DOI：10.1016/j.cam.2011.02.008

• Nonlinear
• Coupled parabolic-hyperbolic system
• High accuracy
• Unconditional stability
• Numerical analysis

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 POE 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.

• 出版日期2011-4-15
• 单位北京应用物理与计算数学研究所