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An Approximate Solution Technique Depending on an Artificial Parameter: A Special Example

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Communications in Nonlinear Science and Numerical Simulation 1998年第2期3卷 40-45页

作者： jihuan he (Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China) Shanghai University Shanghai Institute of Applied Mathematics and Mechanics Shanghai 200072 China

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ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｌａｓｔｔｗｏｄｅｃａｄｅｓｗｉｔｈｔｈｅｒａｐｉｄｄｅｖｅｌｏｐｍｅｎｔｏｆｎｏｎｌｉｎｅａｒｓｃｉｅｎｃｅ，ｔｈｅｒｅｈａｓａｐｐｅａｒｅｄｅｖｅｒｉｎｃｒｅａｓｉｎｇｉｎｔｅｒｅｓｔｏｆｓｃｉｅｎｔｉｓｔｓ...

关键词： perturbation methods homotopy Duffing equation nonlinearity

A Generalized Variational Principle for Coupled Thermoelasticity with Finite Displacement

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Communications in Nonlinear Science and Numerical Simulation 1998年第4期3卷 215-218页

作者： jihuan he Gaolian LIU and Weibing FENG (Institute of Appl. Math. & Mech., Shanghai Uni., Shanghai 200072, China)E--mails glliu@*** Institute of Appl. Math. Mech. Shanghai Uni. Shanghai 200072 China

Via the semi-inverse method proposed by he, a generallied variational principle of classical type (not Gurtin -type & not involving convolutions) for the entitled problem of linear anisotropic materials has been obta... 详细信息

关键词： variational technique thermoelasticity

Preparation and Characterization of TiO2 Nanotubes Decorated by CuO and CeO2 Particles

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Journal of Donghua University(English Edition) 2019年第2期36卷 113-116页

作者： SheN Jiali he jihuan National Engineering Laboratory for Modern Silk College of Textile and Clothing EngineeringSoochow University

A novel catalyst,TiO2 nanotubes(TiO2 NTs)composite decorated by CuO and CeO2 particles,was prepared by a simple and cost-effective *** TiO2 NTs were fabricated by the hydrothermal method,and CuO and CeO2 particles loaded onto TiO2 NTs(CuO/CeO2@TiO2 NTs)were prepared by the water bath heating *** CuO/CeO2@TiO2 NTs were investigated and characterized by transmission electron microscope(TEM),energy dispersive spectrometer(EDS),photoluminescence(PL),X-ray diffractometer(XRD)and ultraviolet-visible light diffuse reflectance spectrum(UV-Vis DRS).Both the p-n heterojunction formed at the p-CuO and n-TiO2 interfaces and the highly induced electron transfer of CeO2 can greatly promote the separation of ***,CuO/CeO2@TiO2 NTs show enhanced absorption and have potential applications in photocatalysis.

关键词： TiO2 nanotubes(TiO2 NTs) CuO CeO2 hydrothermal method

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A New Approach to Nonlinear Partial Differential Equations

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Communications in Nonlinear Science and Numerical Simulation 1997年第4期2卷 230-235页

作者： jihuan he (Shanghai University,Shanghai Institute of Applied Mathematics and Mechanics,Shanghai 2 0 0 0 72 ,China) Shanghai University Shanghai Institute of Applied Mathematics and Mechanics Shanghai 200072 China

In this paper,a novel method called variational iteration method is proposed to solve nonlinear partial differential equations without linearization or small *** this method,a correction functional is constructed by a general Lagrange multiplier,which can be identified via variational *** analytical solution can be obtained from its trial- function with possible unknown constants,which can be identified by imposing the boundary conditions,by successively iteration.

关键词： Nonlinear Problems Partial Differential Equations Variational Iteration Method Variational Theory

Some New Approaches to Duffing Equation with Strongly and High Order Nonlinearity (II) Parametrized Perturbation Technique

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Communications in Nonlinear Science and Numerical Simulation 1999年第1期4卷 78-83页

作者： jihuan he (Shanghai institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China) Email: glliu@*** Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China

For the strongly nonlinear equations without small parameter, a transformation u = v can be introduced for the nonlinear equation L(u) + N(u) = 0, where L and N are general linear and nonlinear differential operators respectively, P is sufficiently small. Therefore, a strongly non-linear system is transformed into a small parameter system with respect to the new introduced parameter P, thus various traditional perturbation techniques can be applied. By Lindstedt-Poincare method, a perturbation solution for Duffing equation with sib order nonlinearity is obtained, which is valid not only for the small parameter E in the equation, but also for very large values of E.

关键词： perturbation technique nonlinear equation

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Variational Iteration Method for Delay Differential Equations

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Communications in Nonlinear Science and Numerical Simulation 1997年第4期2卷 235-236页

作者： jihuan he (Shanghai University,Shanghai Institute of Applied Mathematics and Mechanics,Shanghai 2 0 0 0 72 ,China) Shanghai University Shanghai Institute of Applied Mathematics and Mechanics Shanghai 200072 China

The variational iteration method is shown to be applicable to delay differential equations for analytical approximate solutions

关键词： Variational Iteration Method for Delay Differential Equations

Approximate Analytical Solution of Blasius'Equation

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Communications in Nonlinear Science and Numerical Simulation 1998年第4期3卷 260-263页

作者： jihuan he(Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics,Shanghai 200072, China)Email: glliu@*** Shanghai University Shanghai Institute of Applied Mathematics and Mechanics Shanghai 200072 China

The Blasius’ equation f"’ + ff"/2=0, with boundary conditions f(0) =f,(0)0, f’ (+∞)=1 is studied in this paper. An approximate analytical solution is obtained via the variational iteration method. The comparison w... 详细信息

关键词： nonlinear technique variational iteration method Blasius’ flow variational technique

Variational Approach to a Strictly Hyperbolic System of Conservation Laws with Singularity

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Communications in Nonlinear Science and Numerical Simulation 1998年第3期3卷 179-183页

Via the send-inverse method proposed by he, a variational principle isestablished for a system of two conservation laws which is strictly hyperbolic. Applyingvariational technique with variable-domain, the Rankine-Hug... 详细信息

关键词： variational technique semi-inverse method hyperbolic problems

A Variational Model for an AsymptoticMagnetohydrodynamic System

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Communications in Nonlinear Science and Numerical Simulation 1998年第3期3卷 176-179页

In the present paper an asymptotic gas magnetohydrodynamic system isformulated in veriational principles for the first time via the semi-inverse method proposedby he. Thus, a new theoretical basis for the trite elemen... 详细信息

关键词： variational technique semi-inverse method unsteady flow magnetohydrodynamic