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variable separation method for a nonlinear time fractional partial differential equation with forcing term

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2018年 339卷 297-305页

作者： Zhang, Sheng Hong, Siyu Bohai Univ Sch Math & Phys Jinzhou 121013 Peoples R China

In this paper, a variable-coefficient nonlinear time fractional partial differential equation (PDE) with initial and boundary conditions is solved by using the variable separation method. As a result, some new explicit and exact solutions of the time fractional PDE are obtained including Airy function solution, hyperbolic function solution, trigonometric function solution and rational solution. It is shown that the variable separation method can provide a useful mathematical tool for solving some other nonlinear time fractional PDEs in science and engineering. (C) 2017 Elsevier B.V. All rights reserved.

关键词： variable separation method Time fractional PDE Airy function solution Hyperbolic function solution Trigonometric function solution Rational solution

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variable separation method based Analytical model for Surface potential profile of Triple Material Double Gate MOSFETs

Variable Separation Method based Analytical model for Surfac...

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International Conference on Science Engineering and Management Research (ICSEMR)

作者： Banu, N. Abrose Kavitha, T. Ilahi, K. Ashik NPR Coll Engn & Tech Natham Dindigul India MAVMM Engn Coll SACS Madurai Tamil Nadu India

ISBN: (纸本)9781479976133

The concept of integration of transistors evolves towards smaller line widths. This can be achieved by the prominent Very Large Scale Integration (VLSI) technology. The level of integration of silicon technology as measured in terms of number of devices per IC. This leads to the idea of scaling in MOSFET (Metal Oxide Semiconductor Field Effect Transistor) devices. Scaling enhances the design or manufacturing of extremely small complex circuitry using modified semiconductor material. But eventually scaling leads to short channel effects (SCEs). To enable future technology scaling, new device structures like MULTIGATE MOSFET refers to a MOSFET (metal-oxide-semiconductor field-effect transistor) which includes quite one gate into a sole device have been proposed. These Nano scale devices have a significant potential to scale beyond the perceived scaling limitations of traditional CMOS (Complementary Metal Oxide Semiconductor). The present work involves several distinct features, viz. The main objective is to reduce the Short Channel Effects (SCE) and effects of surface potential variation by using Triple Material Double Gate MOSFET (TMDG) in which the gate is made of three materials with different work functions. For analysing a short channel effects in Triple material double gate MOSFET, a 2-D Analytical channel potential and minimum surface potential is developed by solving the two dimensional Poisson's equation using variable separation method(superposition technique). To simulate surface potential behavior of TMDG, TCAD Simulator is used for investigating novel features offered by the device.

关键词： VLSI MOSFET SCE MULTIGATE MOSFET scaling channel potential minimum surface potential variable separation method TMDG CMOS TCAD

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On the feasibility of variable separation method based on Hamiltonian system for plane magnetoelectroelastic solids

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Chinese Physics B 2008年第8期17卷 2753-2758页

作者：侯国林阿拉坦仓 Department of Mathematics College of Science and Technology Inner Mongolia University

The eigenvalue problem of an infinite-dimensional Hamiltonian operator appearing in the isotropic plane magnetoelectroelastic solids is studied. First, all the eigenvalues and their eigenfunctions in a rectangular domain are solved directly. Then the completeness of the eigenfunction system is proved, which offers a theoretic guarantee of the feasibility of variable separation method based on a Hamiltonian system for isotropic plane magnetoelectroelastic solids. Finally, the general solution for the equation in the rectangular domain is obtained by using the symplectic Fourier expansion method.

关键词： magnetoelectroelastic solid variable separation method completeness general solution

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The variable separation method and exact Jacobi elliptic function solutions for the Nizhnik-Novikov-Veselov equation

ACTA PHYSICA POLONICA A

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ACTA PHYSICA POLONICA A 2006年第1期110卷 3-9页

作者： Peng, Y. -Z. Huazhong Univ Sci & Technol Dept Math Wuhan 430074 Peoples R China

Based on the singular structure analysis, the variable separation method is proposed for the Nizhnik-Novikov-Veselov equation to obtain a general functional separation solution containing three arbitrary functions. Choosing these arbitrary functions to be the Jacobi elliptic functions, a diversity of elliptic function solutions may be obtained for the equation of interest. The interaction property of the waves is numerically studied. The long wave limit gives the new type of localized coherent structures.

关键词： .singular arbitrary Eq long wave structure analysis variable separation method Function Solutions Nizhnik–Novikov–Veselov general functional separation

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Modeling of composite and sandwich beams with a generic cross-section using a variable separation method

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COMPOSITES PART B-ENGINEERING 2019年 165卷 648-661页

作者： Vidal, P. Giunta, G. Gallimard, L. Polit, O. Univ Paris Nanterre UPL LEME F-92410 Ville Davray France Luxembourg Inst Sci & Technol 5 Ave Hauts Fourneaux L-4362 Esch Sur Alzette Luxembourg

In this work, the modeling of laminated composite and sandwich beams with a generic cross-section is performed through a variable separation approach. For this purpose, the displacement is approximated as a sum of separated functions of the cross-section coordinates y, z and the axial coordinate x. This choice yields to a non-linear problem that can be solved by an iterative process. This latter consists of solving a 2D and 1D Finite Element problem successively at each iteration. Numerical examples involving several representative sandwich and laminated beams are addressed to show the accuracy of the present method. It is shown that it can provide 3D results and capture local effects for various types of cross-section.

关键词： Generic cross-section Composite beam variable separation method Finite element solution

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A few kinds of Riccati equation integrable conditions and variable separation method

A few kinds of Riccati equation integrable conditions and va...

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International Conference on Mechatronics Engineering and Computing Technology (ICMECT)

作者： Yin Zhihong Kunming Univ Sci & Technol Fac Mech & Elect Engn Kunming 650500 Yunnan Peoples R China

ISBN: (纸本)9783038351153

Summarizes several types of the Riccati equation can be used in the form of elementary integral form and its general solution. The Riccati equation through the appropriate variable substitution can be variable separable equation, to calculate the general solution to use the method of elementary integrals. Some of these methods need certain skills. With a typical example this paper introduces the basic techniques of variable substitution.

关键词： Riccati equation Integrable condition variable separation method

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Derivation of Radial-Angular Singularity Cancellation Transformations by the variable separation method

Derivation of Radial-Angular Singularity Cancellation Transf...

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International Conference on Electromagnetics in Advanced Applications

作者： Li Li Kun Wang Thomas F. Eibert Lehrstuhl für Hochfrequenztechnik Technische Universit?t München Munich 80290 Germany

ISBN: (纸本)9781479978076

The variable separation method is utilized to derive a family of radial-angular-R~n transformation schemes for singularity cancellation. The variables, the angle and the radius in polar coordinates derived from the Cartesian coordinates, are utilized by the variable separation method. General solutions to the differential equations derived from the variable separation method are proposed. A new family of radial-angular-R~1, -R~2 and -R~3 transformation schemes is designed for the singularity cancellation technique. The proposed transformation schemes are applicable to all types of singular kernels in the method of Moments (MoM) as found in electromagnetic surface integral equations.

关键词： Derivation Radial-Angular Singularity Cancellation Transformations variable separation method

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Symplectic superposition solution for the buckling problem of orthotropic rectangular plates with four clamped edges

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ARCHIVE OF APPLIED MECHANICS 2025年第1期95卷 1-10页

作者： Zhang, Mengmeng Bai, Eburilitu Wang, Jinglong Mongolia Univ Sch Math Sci Inner Hohhot 01002 Peoples R China

The main objective of this study is to uniformly solve the buckling problem of fully clamped (CCCC) orthotropic/isotropic rectangular plates with different thicknesses. The analysis uses the symplectic superposition method. This method describes the buckling problem of orthotropic rectangular moderately thick plates (RMTPs) in the Hamiltonian system for treatment in the symplectic space. First, the governing equations of RMTPs are represented by Hamiltonian canonical equations. Then, the original buckling problem of a CCCC rectangular moderately thick plate (RMTP) is divided into two sub-buckling problems. The variable separation method in the Hamiltonian system is used to calculate the general solutions of these two sub-buckling problems. The symplectic superposition solution of the original buckling problem is obtained by superimposing the general solutions of the two sub-buckling problems. Finally, the analysis results of the buckling load and modal shape of orthotropic rectangular plates under various thicknesses and aspect ratios are presented in numerical examples.

关键词： Buckling problem Symplectic superposition method variable separation method Hamiltonian system Rectangular moderately thick plate

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method of variable separation for investigating exact solutions and dynamical properties of the time-fractional Fokker-Planck equation

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2022年 595卷 127068-127068页

作者： Rui, Weiguo Yang, Xinsong Chen, Fen Chongqing Normal Univ Sch Math Sci Chongqing 401331 Peoples R China Sichuan Univ Coll Elect & Informat Engn Chengdu 610065 Peoples R China

In this paper, the traditional separation method of variables is improved by fixing a part of the variables called the separation method of semi-fixed variables. By using this improved method, the time-fractional Fokker-Planck equation with external force field is studied. Some new exact solutions and dynamical properties of the equation are investigated in various external potential functions such as linear potential, harmonic potential, logarithmic potential, exponential potential, and quartic potential. Some interesting dynamical behaviors and phenomena are discovered. The profiles of several representative exact solutions are illustrated by 3D-graphs and 2D-graphs(C) 2022 Elsevier B.V. All rights reserved.

关键词： Time-fractional Fokker-Planck equation variable separation method Mittag-Leffler function Exact solution and dynamical property Anomalous diffusion

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Wave Radiation and Diffraction by A Two-Dimensional Floating Body with An Opening Near A Side Wall

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China Ocean Engineering 2013年第4期27卷 437-450页

作者：张洪生周华伟 Ocean Environmental and Engineering College Shanghai Maritime University State Key Laboratory of Ocean Engineering College of Naval Architecture Ocean and Civil Engineering Shanghai JiaoTong University

The radiation and diffraction problem of a two-dimensional rectangular body with an opening floating on a semi- infinite fluid domain of finite water depth is analysed based on the linearized velocity potential theory through an analytical solution procedure. The expressions for potentials are obtained by the method of variation separation, in which the unknown coefficients are determined by the boundary condition and matching requirement on the interface. The effects of the position of the hole and the gap between the body and side wall on hydrodynamic characteristics are investigated. Some resonance is observed like piston motion in a moon pool and sloshing in a closed tank because of the existence of restricted fluid domains.

关键词： wave radiation and diffraction floating body with an opening side wall variable separation method domain decomposition

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