A nonlinear fully implicit finite difference scheme with second-order time evolution for nonlinear diffusion problem is *** scheme is constructed with two-layercoupled discretization(TLCD)at each time *** does not st...
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A nonlinear fully implicit finite difference scheme with second-order time evolution for nonlinear diffusion problem is *** scheme is constructed with two-layercoupled discretization(TLCD)at each time *** does not stir numerical oscillation,while permits large time step length,and produces more accurate numerical solutions than the other two well-known second-order time evolution nonlinearschemes,the Crank-Nicolson(CN)scheme and the backward difference formula second-order(BDF2)*** developing a new reasoning technique,we overcome the difficulties caused by the couplednonlineardiscrete 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 *** tests verify the theoretical results,and illustrate its superiority over the CN and BDF2 schemes.
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