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求解二维扩散方程的加权平均隐式多重网格方法 被引量：1

Multigrid Solution Based on Weighted Average Implicit Scheme of the Two Dimensional Diffusion Equation
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摘要 提出了数值求解二维扩散方程两种精度分别为O(τ2+h2)和O(τ2+h4)的无条件稳定的加权平均隐格式,并采用多重网格方法进行求解,从而克服了传统迭代法在求解隐格式时收敛速度慢的缺陷,提高了求解效率.数值实验验证了该方法的精确性和可靠性. Two classes of unconditional stable,weighted average implicit difference schemes for the twodimensional diffusion equation are proposed.Their local truncation errors are O(τ2+h2) and O(τ2+h4) respectively.A multigrid technique is employed to accelerate the convergence speed of traditional relaxation methods and fast solutions are obtained.Numerical experiment is carried out to prove their accuracy and dependability.
作者 葛永斌 吴文权 卢曦
机构地区 上海理工大学动力工程学院
出处 《内蒙古大学学报（自然科学版）》 CAS CSCD 北大核心 2003年第5期490-494,共5页 Journal of Inner Mongolia University：Natural Science Edition
基金 国家自然科学基金资助项目(59876023) 上海市教委青年基金资助项目(02QG22)
关键词 扩散方程 多重网格 加权平均隐格式 无条件稳定 diffusion equation multigrid weighted average implicit scheme unconditional stable
分类号 O241.82 [理学—计算数学]
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参考文献7

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共引文献6

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  • 1王洁,张海良.二维抛物型方程非齐次边值问题的高精度差分格式[J].台州学院学报,2007,29(3):1-3. 被引量：1
  • 2Liu H W, Liu L B, Chen Y. A semi - discretization method based on quartic splines for solving one - space - dimensional hyper-bolic equations [ J ]. Appl Math Comput, 2009,210:508 - 514.
  • 3Gao F, Chi C. Unconditionally stable difference schemes for a one - space dimensional linear hyperbolic equation [ J ]. Appl Math Comput ,2007,187 : 1272 - 1276.
  • 4Ding H, Zhang Y. A new difference scheme with high accuracy and absolute stability for solving convection - diffusion equations [ J ]. J Comput Appl Math ,2009,230:600 - 606.
  • 5Lin Y, Gao X J, Xiao M Q. A high - order finite difference method for 1D nonhomogeneous heat equations [ J ]. Numerical Meth- ods for Partial Differential Equations, 2009,25 : 327 - 346.
  • 6Burg C, Erwin T. Application of Richardson extrapolation to the numerical solution of partial differential equations [ J ]. Numeri- cal Methods for Partial Differential Equations,2009,25:810- 832.
  • 7Karaa S. A high -order ADI method for parabolic problems with variable coeflqcients [ J ]. Inter J Comput Math ,2000 ,86:109 -120.
  • 8Liu J M, Tang K M. A new unconditionally stable ADI compact scheme for the two - space - dimensional linear hyperbolic equa- tion [ J ]. Inter J Comput Math,2010,87 (10) :2259 - 2267.
  • 9Karaa S. Unconditionally stable ADI scheme of higher- order for linear hyperbolic equations[ J]. Inter J Comput Math,2010, 87 ( 13 ) :3030 - 3038.
  • 10Bialecki B, Frntos J. ADI spectral collocation methods for parabolic problems [ J ]. J Comput Phys ,2010,229:5182 -5193.

引证文献1

内蒙古大学学报（自然科学版）
2003年 第5期

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