The 3-Layered Explicit Difference Scheme for 2-D Heat Equation
-
摘要: 对二维热传导方程构造了一个稳定的三层显式差分格式求其数值解,其背景源于高维热力学反问题迭代算法中对正问题小计算量算法的需求。首先建立一个含参数的一般差分格式去逼近微分方程,并得到了最优截断误差。然后导出了参数应满足的条件以保证差分格式的稳定性。最后给出了数值的例子并和其它算法进行比较,说明了格式在精度上的有效性和计算量上的优越性。Abstract: A 3-layered explicit difference scheme for the numerical solution of 2-D heart equation is proposed.Firstly,a general symmetric difference scheme is constructed and its optimal error is obtained.Then two kinds of condition for choosing the parameters for optimal error and stable difference scheme are given.Finally some numerical results are presented to show the advantage of the schemes.
-
Key words:
- parabolic equation /
- difference schemes /
- error estimate /
- stability
-
[1] Smith G D.Numerical Solutions of Partial Differential Equations:Finite Difference Methods[M].New York: Oxford University Press,1985. [2] Munize W B.A comparison of some inverse methods for estimating the initial condition of the heat equation[J].J Comput Appl Math,1999,103:145-163. [3] 周顺兴.解二维和三维抛物型偏微分方程绝对稳定的差分格式,计算数学,1980,9(1):90-97. [4] 孙鸿烈.解高维热传导方程的一族高精度的显示差分格式[J].高校应用数学学报,A辑,1999,14(4):427-432. [5] LIU Ji-jun.Numerical solution of forward and backward problem for 2-D heat conduction equation[J].J Comput Appl Math,2002,145(2):459-482. -
点击查看大图
计量
- 文章访问数: 2774
- HTML全文浏览量: 105
- PDF下载量: 1576
- 被引次数: 0
下载:
