【摘 要】
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A nonlinear fully implicit finite difference scheme with second-order time evolution for nonlinear diffusion problem is studied.The scheme is constructed with two-layer coupled discretization (TLCD) at each time step.It does not stir numerical oscillation
【机 构】
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Laboratory of Computational Physics,Institute of Applied Physics and Computational Mathematics,P.O.B
论文部分内容阅读
A nonlinear fully implicit finite difference scheme with second-order time evolution for nonlinear diffusion problem is studied.The scheme is constructed with two-layer coupled discretization (TLCD) at each time step.It does not stir numerical oscillation,while per-mits large time step length,and produces more accurate numerical solutions than the other two well-known second-order time evolution nonlinear schemes,the Crank-Nicolson (CN)scheme and the backward difference formula second-order (BDF2) scheme.By developing a new reasoning technique,we overcome the difficulties caused by the coupled nonlinear discrete diffusion operators at different time layers,and prove rigorously the TLCD scheme is uniquely solvable,unconditionally stable,and has second-order convergence in both s-pace and time.Numerical tests verify the theoretical results,and illustrate its superiority over the CN and BDF2 schemes.
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