| 一类非线性边界条件的抛物型方程组的周期解的数值解法 |
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| 引用本文： | 陈玉娟.一类非线性边界条件的抛物型方程组的周期解的数值解法[J].数学杂志,2005,25(5):485-493. |
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| 作者姓名： | 陈玉娟 |
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| 作者单位： | 南京师范大学数学系,江苏南京,210097;南通师范大学数理学院,江苏南通,226007 |
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| 基金项目： | Supported by the Natural .Science Foundation of Jiangsu Education 0ffice（03KJD110169） |
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| 摘 要： | 本文研究了一类具有非线性边界条件的反应一扩散一对流方程组的周期解的数值解法，利用上下解作为初始迭代，把求方程组的Jacobi方法和Gauss—Seidel方法和上下解方法结合起来，得到了迭代序列的单调收敛性和方法的收敛性，对方法的稳定性也作了论述。
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| 关 键 词： | 周期解 抛物型方程组 有限差分 收敛性 误差估计 |
| 文章编号： | 0255-7797（2005）05-0485-09 |
| 收稿时间： | 2003-11-12 |
| 修稿时间： | 2003-11-122004-03-18 |
NUMERICAL METHODS FOR PERIODIC SOLUTIONS OF PARABOLIC SYSTEMS WITH NONLINEAR BOUNDARY CONDITIONS |
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| CHEN Yu-juan.NUMERICAL METHODS FOR PERIODIC SOLUTIONS OF PARABOLIC SYSTEMS WITH NONLINEAR BOUNDARY CONDITIONS[J].Journal of Mathematics,2005,25(5):485-493. |
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| Authors: | CHEN Yu-juan |
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| Institution: | Dept. of Math. ,Nanjing Normal University, Nanjing 210097, China;School of Math. and Physics ;Nantong Normal University, Nantong 226007, China |
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| Abstract: | This paper is devoted to numerical methods of periodic solutions for a class of nonlinear reaction-diffusion-convection systems under nonlinear boundary conditions. Combining the method of upper and lower solutions with Jacobi or Gauss-Seidel method, we can gain the monotone convergence of the iterative sequences and the convergence of the methods. The numerical stability of these schemes is also discussed. |
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| Keywords: | periodic solution parabolic systems finite difference convergence error estimates |
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