| 用线方法求解带混合边值条件的抛物方程 |
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| 引用本文： | 梁燕来,屈小妹,吴庆军,蒙诗德.用线方法求解带混合边值条件的抛物方程[J].数学的实践与认识,2008,38(17). |
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| 作者姓名： | 梁燕来 屈小妹 吴庆军 蒙诗德 |
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| 作者单位： | 1. 玉林师范学院,数学与计算机科学系,广西,玉林,537000
2. 玉林师范学院,数学与计算机科学系,广西,玉林,537000;华中科技大学,数学与统计学院,湖北,武汉,430074 |
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| 基金项目： | 国家自然科学基金，广西教育厅科研项目 |
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| 摘 要： | 研制了分别用显式Euler法、隐式Euler法、Crank-Nicolson格式(梯形方法)求解带第一、第二及混合边值条件的抛物问题的应用软件,通过求解若干抛物问题对该软件作了测试,获得了预期的数值结果,讨论了时间和空间步长的变化对格式计算结果的影响,得到了三种方法的稳定性、收敛精度和计算量.
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| 关 键 词： | 显式Euler法 隐式Euler法 梯形方法 抛物方程 半离散问题 |
Numerical Simulation of Parabolic Equations with the Mixed Boundary Condition in the Method of Line |
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| LIANG Yan-lai,QU Xiao-mei,WU Qing-jun,MENG Shi-de.Numerical Simulation of Parabolic Equations with the Mixed Boundary Condition in the Method of Line[J].Mathematics in Practice and Theory,2008,38(17). |
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| Authors: | LIANG Yan-lai QU Xiao-mei WU Qing-jun MENG Shi-de |
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| Abstract: | In this thesis,the method of line is applied to solve the initial boundary-value problems for parabolic equations.The explicit Euler method,the implicit Euler method and the Crank-Nicolson scheme are used for the time discretization respectively.A numerical software which is suitable for solving this kind of problems has been developed.Several numerical experiments are carried out by using this software,and it indicates that the numerical solutions agree with the analytic solution quite well.Stability and convergence for the three methods are compared with the help of numerical experiments. |
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| Keywords: | explicit Euler method implicit Euler method trapezoidal scheme parabolic equation semi-discrete problem |
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