• 论文 • 上一篇    下一篇

一维抛物型方程第三边值问题的紧有限体积格式

王风娟, 王同科   

  1. 天津师范大学数学科学学院, 天津 300387
  • 收稿日期:2012-04-09 出版日期:2013-03-15 发布日期:2013-03-12
  • 基金资助:

    国家自然科学基金(11071123)资助项目.

王风娟, 王同科. 一维抛物型方程第三边值问题的紧有限体积格式[J]. 数值计算与计算机应用, 2013, 34(1): 59-74.

Wang Fengjuan, Wang Tongke. COMPACT FINITE VOLUME SCHEME FOR ONE DIMENSIONAL PARABOLIC EQUATIONS WITH THIRD BOUNDARY CONDITIONS[J]. Journal of Numerical Methods and Computer Applications, 2013, 34(1): 59-74.

COMPACT FINITE VOLUME SCHEME FOR ONE DIMENSIONAL PARABOLIC EQUATIONS WITH THIRD BOUNDARY CONDITIONS

Wang Fengjuan, Wang Tongke   

  1. School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, China
  • Received:2012-04-09 Online:2013-03-15 Published:2013-03-12
本文针对一维抛物型方程第三边值问题提出了一种紧有限体积格式, 该格式形成的线性代数方程组具有对称三对角性质, 且不可约占优, 可以使用追赶法求解.证明了格式按照离散L2范数在空间方向具有3.5阶精度, 在时间方向具有2阶精度. 数值算例验证了理论分析的正确性, 并说明了格式的有效性.
In this paper, a compact finite volume scheme is presented for one dimensional parabolic equations with third boundary conditions. The linear algebraic system derived by this scheme has symmetrically tridiagonal property and can be solved by Thomas method. It is proved that the given scheme is convergent with 3.5-order accuracy in spatial direction and secondorder accuracy in temporal direction with respect to discrete L2 norm. Numerical examples verify the correctness of the theoretical analysis and also show the effectiveness of the scheme.

MR(2010)主题分类: 

()
[1] Sun Zhizhong. An unconditionally stable and O(τ2+h4) order L convergent difference scheme for linear parabolic equations with variable coefficients[J]. Numerical Methods for Partial Differential Equations, 2001, 17(6): 619-631.
[2] Qin Jinggang, Wang Tongke. A compact locally one-dimensional finite difference method for nonhomogeneous parabolic differential equations[J]. International Journal for Numerical Methods in Biomedical Engineering, 2011, 27: 128-142.
[3] Li J, Chen Y, Liu G. High-order compact ADI methods for parabolic equations[J]. Computers and Mathematics with Applications, 2006, 52: 1343-1356.
[4] Zhao Jennifer, Dai Weizhong, Niu Tianchan. Fourth-order compact schemes of a heat conduction problem with Neumann boundary condition[J]. Numerical Methods for Partial Differential Equations, 2007, 23: 949-959.
[5] Sun Zhizhong. Compact difference schemes for heat equation with Neumann boundary conditions[ J]. Numerical Methods for Partial Differential Equations, 2009, 25: 1320-1341.
[6] Liao W Y, Zhu J P, and Khaliq A Q M. A fourth-order compact algorithm for nonlinear reaction diffusion equations with Neumann boundary conditions[J]. Numerical Methods for Partial Differential Equations, 2006, 22: 600-616.
[7] Dai Weizhong. A new accurate finite difference scheme for Neumann (insulated) boundary condition of heat conduction[J]. International Journal of Thermal Sciences, 2010, 49: 571-579.
[8] Dai Weizhong, Da Yu Tzou. A fourth-order compact finite difference scheme for solving an NCarrier system with Neumann boundary conditions[J]. Numerical Methods for Partial Differential Equations, 2010, 26: 274-289.
[9] Dai Weizhong. An improved compact finite difference scheme for solving an N-Carrier system with Neumann boundary conditions[J]. Numerical Methods for Partial Differential Equations, 2010, 26: 436-446.
[10] 王同科. 一维二阶椭圆和抛物型微分方程的高精度有限体积元方法[J].数值计算与计算机应用, 2002, 23(4): 264-274.
[11] Gao Guanghua, Wang Tongke. Cubic superconvergent finite volume element method for onedimensional elliptic and parabolic problem[J]. Journal of Computational and Applied Mathematics, 2010, 233: 2285-2301.
[12] 崔吉田, 王同科. 两点混合边值问题的紧有限体积格式[J].应用数学, 2012, 23(1): 96-104.
[1] 邱亚南, 王娜, 刘东杰. 扇形区域外问题的自适应边界元方法[J]. 数值计算与计算机应用, 2021, 42(4): 337-350.
[2] 陈键铧, 阳莺. 一类线性Poisson-Boltzmann方程的虚单元法[J]. 数值计算与计算机应用, 2021, 42(3): 237-246.
[3] 葛志昊, 李婷婷, 王慧芳. 双资产欧式期权定价问题的特征有限元方法[J]. 数值计算与计算机应用, 2020, 41(1): 27-41.
[4] 洪旗, 苏帅. 任意四边形网格上扩散问题的一个稳定九点格式[J]. 数值计算与计算机应用, 2019, 40(1): 51-67.
[5] 杨宇博, 马和平. 广义空间分数阶Burgers方程的Legendre Galerkin-Chebyshev配置方法逼近[J]. 数值计算与计算机应用, 2017, 38(3): 236-244.
[6] 李焕荣. 二维土壤水中溶质运移问题的全离散混合元法研究[J]. 数值计算与计算机应用, 2012, 33(3): 207-214.
[7] 王同科. 一类二维粘性波动方程的交替方向有限体积元方法[J]. 数值计算与计算机应用, 2010, 31(1): 64-75.
[8] 刘会坡,严宁宁. Stokes方程最优控制问题的超收敛分析[J]. 数值计算与计算机应用, 2006, 27(4): 281-291.
阅读次数
全文


摘要