A compact difference scheme combined with extrapolation techniques for solving a class of neutral delay parabolic differential equations
A compact difference scheme combined with extrapolation techniques for solving a class of neutral delay parabolic differential equations
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DOI：
10.1016/j.aml.2012.09.015
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发表时间：
2013-02-01
影响因子：
3.7
通讯作者：
Zhang, Chengjian
中科院分区：
文献类型：
--
作者：
Zhang, Qifeng;Zhang, Chengjian
在这项工作中，我们提出了一种隐式紧致差分格式来求解一类中性时滞抛物型微分方程（NDPDE）。证明了该格式的唯一可解性和无条件稳定性。通过针对线性和非线性问题使用不同的Richardson外推技术，提高了该方案的时间精度，在时间和空间维度上均获得了四阶精度。最后进行数值实验验证算法的准确性和效率。 (C) 2012 Elsevier Ltd. 保留所有权利。
In this work, we present an implicit compact difference scheme for solving a class of neutral delay parabolic differential equations (NDPDEs). The unique solvability and unconditional stability of the scheme are proved. The temporal accuracy of the scheme is improved by using different Richardson extrapolation techniques for linear and nonlinear problems, and fourth-order accuracy in both temporal and spatial dimensions is obtained. Finally, numerical experiments are conducted to verify the accuracy and efficiency of the algorithms. (C) 2012 Elsevier Ltd. All rights reserved.