The high-order multistep ADI solver for two-dimensional nonlinear delayed reaction-diffusion equations with variable coefficients
The high-order multistep ADI solver for two-dimensional nonlinear delayed reaction-diffusion equations with variable coefficients
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DOI：
10.1016/j.camwa.2018.02.017
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发表时间：
2018-05
期刊：
影响因子：
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通讯作者：
Jianqiang Xie;Zhiyue Zhang
中科院分区：
文献类型：
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作者：
Jianqiang Xie;Zhiyue Zhang
构造并分析了二维变系数非线性延迟反应扩散方程的高阶紧致多步交替方向隐式(ADI)格式。利用离散能量方法，证明了在无约束时间网格中，O(τ2+hx4+hy4)关于H1范数和L 2范数的收敛速度是无条件稳定的。最后，数值结果证明了我们的ADI求解器的有效性，并证明了理论结果的正确性。
In this paper, a high-order compact multistep alternating direction implicit (ADI) difference scheme is constructed and analyzed for two-dimensional (2D) nonlinear delayed reaction–diffusion equations (NDREs) with variable coefficients. By the discrete energy method, it is presented that it achieves the convergence rate of O (τ 2+ h x 4+ h y 4) with respect to H 1-and L 2-norms in non-constrained temporal grids, and is unconditionally stable. Finally, numerical results demonstrate the effectiveness of our ADI solver and exhibit the correctness of theoretical results.