Numerical Method of Lines
Numerical Method of Lines
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直线数值法
DOI：
10.1007/978-94-011-4635-7_6
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发表时间：
1999
影响因子：
8.8
通讯作者：
Z. Kamont
中科院分区：
文献类型：
--
作者：
Z. Kamont
偏微分方程组的直线法是用差分式代替空间导数。然后将偏方程转化为常微分方程组。该方法用于用常方程解(91,153,219,220,222,225,238)逼近抛物型非线性微分方程组的解。该方法也可作为证明抛物型方程[223,224,227]或一阶双曲组[101,157]所对应的微分问题存在定理的工具。文献[29,108,128]中考虑了非线性泛函微分方程组的线法的简单例子。高阶方程的方法在文[91]中进行了研究。这本书[189]展示了许多使用线的数值方法的例子。文献[186]研究了由直线数值方法产生的一步差分方法的收敛分析。
The method of lines for partial differential equations consists in replacing spatial derivatives by difference expressions. Then the partial equation is transformed into a system of ordinary differential equations. The method is used for approximation of solutions of nonlinear differential problems of parabolic type by solutions of ordinary equations ([91, 153, 219, 220, 222, 225, 238]). The method is also treated as a tool for proving of existence theorems for differential problems corresponding to parabolic equations [223, 224, 227] or first-order hyperbolic systems [101, 157]. Simple examples of the method of lines for nonlinear functional differential equations were considered in [29, 108, 128]. The method for equations of higher orders is studied in [91]. The book [189] demonstrates lots of examples of the use of the numerical method of lines. Convergence analysis of one step difference methods generated by the numerical method of lines was investigated in [186].