| 基于不同分裂的修正局部Crank-Nicolson方法对一维热传导方程的应用 |
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| 引用本文： | 郭瑞,阿布都热西提·阿布都外力. 基于不同分裂的修正局部Crank-Nicolson方法对一维热传导方程的应用[J]. 兵团教育学院学报, 2011, 21(2): 75-78,84 |
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| 作者姓名： | 郭瑞 阿布都热西提·阿布都外力 |
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| 作者单位： | 1. 石河子大学王单学院,新疆石河子,832003
2. 新疆大学数学与系统科学学院,新疆乌鲁木齐,830046 |
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| 基金项目： | 新疆高校科研计划资助项目，国家自然科学基金 |
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| 摘 要： | 本文采用不同分裂的修正局部Crank-Nicolson方法讨论了一维热传导方程的初边值问题。该方法不仅具有原来计算量少，无条件稳定的优点，而且推广了该方法对复杂的数学物理方程应用的可能性。理论上分析了无条件稳定性、相容性及收敛性，最后进行数值试验，验证了它的可行性。
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| 关 键 词： | 不同分裂的修正局部Crank-Nicolson法 无条件稳定性 相容性 收敛性 热传导方程． |
Application of the Modified Local Crank - Nicolson Method for Solving the one - dimensional heat Equation based on the different division |
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| GUO Rui,Abdurexiti Abduwaili. Application of the Modified Local Crank - Nicolson Method for Solving the one - dimensional heat Equation based on the different division[J]. Journal of Bingtuan Education Institute, 2011, 21(2): 75-78,84 |
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| Authors: | GUO Rui Abdurexiti Abduwaili |
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| Affiliation: | GUO Rui1,Abdurexiti Abduwaili2 (1.Teachers College,Shihezi University,Shihezi,Xinjiang 832003,China,2.College of Mathmatics and System Science,Xinjiang University,Urmqi,Xinjiang 830046 China) |
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| Abstract: | This paper uses the modified local Crank - Nicolson method to solve the one - dimensional initial - boundary value problem of heat equation based on different divisions. This method not only has the advantage of little calculation and unconditional stability, but also develops the method to be used to solve more complicate equations of mathematical physics. Unconditional stability, compatibility and convergence are discussed in theoretical. Finally, verify correctness of it with numerical experiments. |
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| Keywords: | modified local Crank - Nicolson method unconditional stability compatibility convergence heat equation |
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