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求解非线性时滞双曲型偏微分方程的紧致差分方法及Richardson外推算法 被引量：1

A COMPACT DIFFERENCE SCHEME AND RICHARDSON EXTRAPOLATION ALGORITHM FOR SOLVING A CLASS OF THE NONLINEAR DELAY HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS
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摘要 本文构造了一类求解非线性时滞双曲型偏微分方程的紧致差分格式,获得了该差分格式的唯一可解性,收敛性和无条件稳定性,收敛阶为O(Γ~2+h^4),并进一步对时间方向进行Richardson外推,使得收敛阶达到了O(Γ~4+h^4).数值实验表明了算法的精度和有效性. In this paper, a class of compact difference schemes are constructed to solve the nonlin- ear delay hyperbolic partial differential equations. The unique solvability, convergence and unconditional stability of the scheme are obtained. The convergence order is O（T2-h4）. Furthermore, the Richardson extrapolation is applied to improve the temporal accuracy of the scheme, and a solution of order four in both temporal and spatial dimensions is obtained. Numerical example shows the accuracy and efficiency of the algorithms.
作者 张启峰 张诚坚 邓定文
机构地区 华中科技大学数学与统计学院 南昌航空大学数学与信息科学学院
出处 《数值计算与计算机应用》 CSCD 2013年第3期167-176,共10页 Journal on Numerical Methods and Computer Applications
基金 国家自然科学基金资助项目(11171125) 国家自然科学基金重大研究计划重点项目(9113000) 湖北省自然科学基金资助项目(2011CDB289) 国家留学基金项目(201306160037)
关键词 紧致差分格式 唯一性 稳定性 收敛性 RICHARDSON外推 Compact difference scheme Solvability Convergence Stability Richard-son extrapolation
分类号 O241.82 [理学—计算数学]
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参考文献17

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二级参考文献19

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数值计算与计算机应用
2013年 第3期

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