| 带非局部边界条件的非线性抛物方程的隐式差分解法 |
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| 引用本文： | 万正苏,陈光南.带非局部边界条件的非线性抛物方程的隐式差分解法[J].计算数学,2008,30(4):417-424. |
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| 作者姓名： | 万正苏 陈光南 |
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| 作者单位： | 1. 湖南理工学院数学系,湖南,岳阳,414006
2. 北京应用物理与计算数学研究所,北京,100088 |
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| 基金项目： | 国家自然科学基金项目
，
湖南省教育厅优秀青年基金项目
，
湖南省重点学科建设项目资助
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| 摘 要： | 在准静态弹性力学中常遇到求解带有非局部边界条件的抛物方程初边值问题.本文构造了一个数值求解带有非局部边界条件的非线性抛物方程的隐式差分格式,利用离散泛函分析的知识和不动点定理证明了差分解是存在的,且在离散最大模意义下关于时间步长一阶收敛,关于空间步长二阶收敛,并给出了数值算例.
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| 关 键 词： | 非局部边界条件 非线性抛物方程 隐式差分格式 收敛性 |
THE IMPLICIT DIFFERENCE SCHEME FOR THE NONLINEAR PARABOLIC EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS |
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| Wan Zhengsu,Chen Guangnan.THE IMPLICIT DIFFERENCE SCHEME FOR THE NONLINEAR PARABOLIC EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS[J].Mathematica Numerica Sinica,2008,30(4):417-424. |
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| Authors: | Wan Zhengsu Chen Guangnan |
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| Institution: | Department of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, China;Institute of Applied Physics and Computational Mathematics, Beijing 100088, China |
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| Abstract: | Parabolic equations with nonlocal boundary conditions arise from quasi-static elasticity, electrochemistry and etc. In this paper, we construct an implicit finite difference scheme for the nonlinear parabolic equation with nonlocal boundary conditions. Moreover, using the discrete functional analysis and the fixed-point theorem, we prove that the numerical solution is exist and convergent with the convergence order $O(\tau +h^2)$ in the $L_{\infty}$-norm. Numerical examples are given to illustrate the theoretical results. |
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| Keywords: | nonlocal boundary condition nonlinear parabolic equation implicit difference scheme convergence |
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