An Extrapolation Method of Crank-Nicolson Finite Difference Scheme for Distributed Control Equation
This paper studies a finite difference scheme for the distributed control equation, which is based on Crank-Nicolson finite difference scheme and is constructed by applying an extrapolation technique to the nonlinear term. We proved the existence, uniqueness and convergence of the numerical solution. In literature review, there is no report of theoretical studies about the extrapolation. Meanwhile, these theoretical studies are confirmed by numerical experiments in the end. These show that the scheme is a practical numerical method for some computations or numerical simulations which require less accuracy and less computational time.
KeywordsExtrapolation method Finite difference scheme Distributed control equation Existence Uniqueness Convergence
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