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直接积分非线性常微分方程组两点边值问题的一种数值解法

冯桂云,曲文孝   

  1. 西南物理研究所 ;西南物理研究所
  • 出版日期:1985-03-20 发布日期:1985-03-20

冯桂云,曲文孝. 直接积分非线性常微分方程组两点边值问题的一种数值解法[J]. 数值计算与计算机应用, 1985, 6(3): 135-142.

A NUMERICAL METHOD FOR SOLVING A TWO-POINT BOUNDARY VALUE PROBLEM BY DIRECTLY INTEGRATING NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS

  1. Feng Gui-yun Qu Wen-xiao(Southwestern Institute of Physics, Leshan, Sichuan, China)
  • Online:1985-03-20 Published:1985-03-20
§1.把两点边值问题转化为解多元非线性方程组的算法 文[1]在研究带偏滤器的托卡马克装置等离子体稳态径向输运时,得到等离子体内n、T满足的输运方程和边值条件是
Starting from the problem of the steady radial plasma transport in tokamak devices with divertor, we discuss a numerical method for solving a two-point boundary value problem by directly integrating nonlinear ordinary differential equations. The problem in question is reduced to one of solving a set of nonlinear equations by expanding their integral formal solution in terms of a set of orthogonal functions. When the cosine functions are taken to be.orthogonal funtions, special techniques are presented for numerical calculations of the multiple integrals with single variable limit and for solving transcendental equations whose root covers a wide range and for numerically solving systems of nonlinear equations. These techniques make our method more economical of computation. The method offered can, at least in principle, be extended to solve other two-point boundary value problems of the same class.
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[1] 曲文孝,冯桂云,带偏滤器的托卡马克装置等离子体稳态径向输运的数值解,核聚变与等离子体物理,2. 203(1982) .
[2] A.H. Stround, Approximate Calculation of multiple integrals, prentice Hall Series in Automatic Computation, (1971) .
[3] P. J. Davis, P. Rabinowitz, Methods of numerical integration, Blaisdell Waltham, Mass (1975) .
[4] 徐利治,周蕴时,高维数值积分,科学出版社,(1980) .
[5] 管梅谷,从货郎担问题谈起--评价苏联数学家哈奇扬的一项研究成果,自然杂志,1981,825-827.
[6] G.D. Byrne, C. A. Hall, Numerical Solution of Systems of nonlinear algebraic equations, N. Y. and London, Academic Press, (1973) 281-338.
[7] 沈阳计算所等合编,电子计算机常用算法,科学出版社 1976,336-348.
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