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Compact Difference Method for Time-Fractional Neutral Delay Nonlinear Fourth-Order Equation

Compact Difference Method for Time-Fractional Neutral Delay Nonlinear Fourth-Order Equation
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摘要 In this paper, we present a compact finite difference method for a class of fourth-order nonlinear neutral delay sub-diffusion equations in two-dimensional space. The fourth-order problem is first transformed into a second-order system by a reduced-order method. Next by using compact operator to approximate the second order space derivatives and L2-1σ formula to approximate the time fractional derivative, the difference scheme which is fourth order in space and second order in time is obtained. Then, the existence and uniqueness of solution, the convergence rate of and the stability of the scheme are proved. Finally, numerical results are given to verify the accuracy and validity of the scheme. In this paper, we present a compact finite difference method for a class of fourth-order nonlinear neutral delay sub-diffusion equations in two-dimensional space. The fourth-order problem is first transformed into a second-order system by a reduced-order method. Next by using compact operator to approximate the second order space derivatives and L2-1σ formula to approximate the time fractional derivative, the difference scheme which is fourth order in space and second order in time is obtained. Then, the existence and uniqueness of solution, the convergence rate of and the stability of the scheme are proved. Finally, numerical results are given to verify the accuracy and validity of the scheme.
作者 Huan Wang Qing Yang Huan Wang;Qing Yang(School of Mathematics and Statistics, Shandong Normal University, Jinan, China)
出处 《Engineering(科研)》 CAS 2022年第12期544-566,共23页 工程(英文)(1947-3931)
关键词 Two-Dimensional Nonlinear Sub-Diffusion Equations Neutral Delay Compact Difference Scheme CONVERGENCE Stability Two-Dimensional Nonlinear Sub-Diffusion Equations Neutral Delay Compact Difference Scheme Convergence Stability
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