| 一般FPK方程近似求解的局部Galerkin方法 |
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| 引用本文： | 鄂国康.一般FPK方程近似求解的局部Galerkin方法[J].上海大学学报(英文版),1999,3(1):25-29. |
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| 作者姓名： | 鄂国康 |
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| 作者单位： | Civil Engineering Institute，Southwest Jiaotong University; Faculty of Science and Technology，University of Macao |
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| 摘 要： | １ Ｉｎｔｒｏｄｕｃｔｉｏｎ Ｔｈｅｓｔｏｃｈａｓｔｉｃｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ（ＳＤＥ）ａｒｅｕｓｅｄｉｎｍａｎｙａｒｅａｓｏｆｓｃｉｅｎｃｅａｎｄｅｎｇｉｎｅｅｒｉｎｇ．ＴｈｅｍａｉｎｐｕｒｐｏｓｅｆｏｒｓｏｌｖｉｎｇｐｒｏｂｌｅｍｓｗｉｔｈＳＤＥｉｓｔｏｏｂｔａｉｎｔｈｅｐｒｏｂａｂｉｌｉｔｙｄｅｎｓｉｔｙｆｕｎｃｔｉｏｎ（ＰＤＦ）ｏｆｔｈｅｓｔａｔｅｖａｒｉａｂｌｅｓｇｏｖｅｒｎｅｄｂｙｔｈｅＳＤＥｂｅｃａｕｓｅｍａｎｙｏｔｈｅｒｓｔａｔｉｓｔｉｃａｌａｎａｌｙｓｉｓａ…
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| 收稿时间： | 23 June 1998 |
Local galerkin method for the approximate solutions to general FPK equations |
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| Guokang Er Ph. D..Local galerkin method for the approximate solutions to general FPK equations[J].Journal of Shanghai University(English Edition),1999,3(1):25-29. |
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| Authors: | Guokang Er Ph D |
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| Institution: | Civil Engineering Institute, Southwest Jiaotong University,Faculty of Science and Technology, University of Macao |
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| Abstract: | In this paper, the method proposed recently by the author for the solution of probability density function (PDF) of nonlinear
stochastic systems is presented in detail and extended for more general problems of stochastic differential equations (SDE),
therefore the Fokker-Planck-Kolmogorov (FPK) equation is expressed in general form with no limitation on the degree of nonlinearity
of the SDE, the type of δ-correlated excitations, the existence of multiplicative excitations, and the dimension of SDE or
FPK equation. Examples are given and numerical results are provided for comparing with known exact solution to show the effectiveness
of the method.
The paper partially supported by the Foundation of the Research Committee of the University of Macao (No. 6851/96/UM, 628/97/UM) |
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| Keywords: | stochastic differential equations probability density function FPK equation approximate PDF solution local Galerkin method |
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