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Chinese Physics B 2018年第10期27卷 123-129页

作者：焦小玉 School of Applied Mathematics Nanjing University of Finance and Economics

In this paper, the（2＋1）-dimensional perturbed Boussinesq equation is transformed into a series of two-dimensional（2 D） similarity reduction equations by using the approximate symmetry method. A step-by-step procedure is used to acquire Jacobi elliptic function solutions to these similarity equations, which generate the truncated series solutions to the original perturbed Boussinesq equation. Aside from some singular area, the series solutions are convergent when the perturbation parameter is diminished.

关键词： approximate symmetry method (2+1)-dimensional perturbed Boussinesq equation series solutions convergence of series solutions

Fundamentals and progress of the manifold method based on independent covers

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Science China(Technological Sciences) 2024年第4期67卷 966-991页

作者： SU HaiDong LIN ShaoZhong XIE ZhiQiang GONG YaQi QI YongFeng Material and Engineering Structure Department Yangtze River Scientific Research InstituteWuhan 430010China Research Center of Water Engineering Safety and Disaster Prevention of Ministry of Water Resources Wuhan 430010China

Aiming to solve mesh generation,computational stability,accuracy control,and other problems encountered with existing numerical methods,such as the finite element method and the finite volume method,a new numerical computational method for continuum mechanics,namely the manifold method based on independent covers(MMIC),is proposed based on the concept of mathematical manifolds,to form partitioned series solutions of partial differential *** partitions,the cover meshes have the characteristics of arbitrary shape,arbitrary connection,and arbitrary *** are expected to fundamentally solve the mesh generation problem and can also simulate the precise geometric boundaries of the CAD model and strictly impose boundary *** the selection of series solutions,local analytical solutions(such as series solutions at crack tips and series solutions in infinite domains)or proper forms of complete series can be used to reflect the local or global characteristics of the physical field to accelerate *** applications are presented.A new method of beam,plate,and shell analysis is *** deformation characteristics of beams,plates,and shells are simulated with polynomial series of suitable forms,and the analysis of curved beams and shells with accurate geometric representation is *** the static elastic analysis of two-dimensional structures,a mesh splitting algorithm is proposed,and h-p version adaptive analysis is carried out with error ***,automatic computation integrated with CAD is *** analysis is also attempted for the solution of differential equations of *** the one-dimensional convection-diffusion equation and Burgers equation,calculation results with high precision are obtained in strong convection and shock wave simulations,avoiding nonphysical *** solving the two-dimensional incompressible Navier-Stokes equation is also *** series solution formula is used to o

关键词： series solutions mesh generation adaptive analysis fixed meshes numerical manifold method

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Nonlinear oscillations with parametric excitation solved by homotopy analysis method

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Acta Mechanica Sinica 2008年第3期24卷 325-329页

作者： Jianmin Wen Zhengcai Cao School of Shipbuilding Engineering Harbin Institute of Technology at WeihaiWeihai 264209 China CIMS Research Center Tongji University Shanghai 200092 China

An analytical technique, namely the homotopy analysis method （HAM）, is used to solve problems of nonlinear oscillations with parametric excitation. Unlike perturbation methods, HAM is not dependent on any small physical parameters at all, and thus valid for both weakly and strongly nonlinear problems. In addition, HAM is different from all other analytic techniques in providing a simple way to adjust and control convergence region of the series solution by means of an auxiliary parameter h. In the present paper, a periodic analytic approximations for nonlinear oscillations with parametric excitation are obtained by using HAM, and the results are validated by numerical simulations.

关键词： Nonlinear oscillation Parametric excitation series solutions Homotopy analysis method

Newtonian heating in stagnation point flow of Burgers fluid

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Applied Mathematics and Mechanics(English Edition) 2015年第1期36卷 61-68页

作者： T.HAYAT S.ALI M.AWAIS M.S.ALHUTHALI Department of Mathematics Quaid-i-Azam University Nonlinear Analysis and Applied Mathematics (NAAM) Research Group Faculty of Science King Abdulaziz University Faculty of Engineering Sciences Ghulam Ishaq Khan Institute of Engineering Sciences and Technology Department of Mathematics COMSATS Institute of Information Technology

The Newtonian heating effects in the stagnation point flow of a Burgers fluid are addressed in this paper. The boundary layer flow problems are stated in the spatial domain from zero to infinity. The solution expressions for the velocity and the temperature are obtained and examined for the influential variables. The tabulated values show comparison with the previous results. It is observed that the obtained results are in good agreement with the existing results in limiting sense.

关键词： Burgers fluid Newtonian heating series solutions

Adomian Modification Methods for the Solution of Chebyshev’s Differential Equations

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Applied Mathematics 2023年第8期14卷 512-530页

作者： Mariam Al Mazmumy Aishah Alsulami Huda Bakodah Nawal Alzaid Department of Mathematics College of Science University of Jeddah Jeddah Saudi Arabia

The current study examines the important class of Chebyshev’s differential equations via the application of the efficient Adomian Decomposition Method (ADM) and its modifications. We have proved the effectiveness of the employed methods by acquiring exact analytical solutions for the governing equations in most cases;while minimal noisy error terms have been observed in a particular method modification. Above all, the presented approaches have rightly affirmed the exactitude of the available literature. More to the point, the application of this methodology could be extended to examine various forms of high-order differential equations, as approximate exact solutions are rapidly attained with less computation stress.

关键词： ADM Modifications Methods Chebyshev’s Differential Equations IVPs series solutions