| 用最小p—幂泛函求解微分和积分微分方程(英文) |
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| 作者单位： | Tianjin 300073，P. R. China |
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| 摘 要： | 在微分和积分—微分方程中的很多问题没有自然的能量变分形式,例如,流体力学的Navier—stokes方程中的许多问题。本文提出了用最小p-幂泛函方法去求它们的近似解,同时给出了有关解的存在性和唯一性的回答。文中给出了数值例子,采用最速下降抛物线法将泛函极小化。文中提出了以下概念:正则解,广义解,正则近似解和广义近似解,并用模糊数学理论对广义近似解定义了可靠性的估计,这对于分析计算结果很有利。
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| 关 键 词： | 微分和积分-微分方程 最小p-幂泛函法 模糊理论 |
To Solve Differential and Integro—Differential Equations by Using a Least p—Power Functional |
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| Huang Chenggui. To Solve Differential and Integro—Differential Equations by Using a Least p—Power Functional[J]. Journal of Changzhou Institute of Technology, 1997, 0(4) |
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| Authors: | Huang Chenggui |
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| Affiliation: | Huang ChengguiDepartment of Mathematics Tianjin Normal University |
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| Abstract: | Many problems in differential and integro-differential equations have no natural energy variational forms,for example,various problems in Fluid Mechanics in view of Navier-Stokes Equation. The paper put forward a least p - power functional to solve their approximate solutions, while to answer the existency and u-niqueness. Numerical examples are given. The paper introduces a method of steepest decent parabolic to solve the minmum point of the functional. Besides the paper introduces the concepts:regular solution,general solution,regular approximate solution and general approximate solution and the estimate of reliability of general approximate solution by using fuzzy theory which gives advantages to analyze the results. |
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| Keywords: | differential and integro - differential equations least p - power functional discretizing of a problem steepest decent parabolica integral analysis for a computation nonlinear ordinary differential equations have'nt any real solution but |
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