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AN ARTIFICIAL BOUNDARY CONDITION FOR THE INCOMPRESSIBLE VISCOUS FLOWS IN A NO-SLIP CHANNEL

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Journal of Computational Mathematics 1995年第1期13卷 51-63页

作者： Han Hou-de Bao Wei-zhu(Department of Applied Mathematics, Tsinghua University, Beijing, China) 清华大学应用数学系北京

The numerical simulation of the steady incompressible viscous flows in a no-slip channel is considered. A discrete artificial boundary condition on a given segmental artificial boundary is designed by the method of lines. Then the original problem is reduced to a boundary value problem of Navier-Stokes equations on a bounded domain. The numerical examples show that this artificial boundary condition is very effective and more accurate than Dirichlet and Neumann boundary conditions used in engineering literature.

关键词： Boundary conditions Viscous flow Eigenvalues Approximation Navier Stokes equation polynomials Ordinary differential equations

Population dynamics between a prey and a predator using spectral collocation method

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International Journal of Biomathematics 2019年第5期12卷 19-41页

作者： Sagithyn Thirumalai Rajeuwari Seshadri Suayip Yuzbasi Department of Mathematics Pondicherry UniversityIndia Department of Mathematicst Facviiy of Science Akdeniz University Tr-07058AntalyaTurkey

The struggle for the existence of the biological species is a well-known Prey-Predator model study in the literature.In this study,we present an improved model of Jerri [J.Abdul,Introduction to Integral Equations with Applications,Vol.10 (Wiley,New York,1999)] by introducing the intra-species competition term between the same species in additiuu to the existing environmental changeb and lew other factors in the model.The derntmcl from the exiting (limited) retjources arid other requirements induces competition between the same species which may after the survival tactics among themselves.This intra species term provides strength to tho model ns it makes the model moro realistic.The governing equations are a system of two nonlinear delay integro differential pqimtions,which are solved using spectral collocation method.The role of intra-species coefficients denoting the logistic growth/decay of the two species and two other parameters affecting the population dynamics are analyzed with the three basis functions such as Chebyshev,Legendre and Jacobi polynomials.With the help of simple matrix analysis,the governing equations are converted into a system of nonlinear algebraic equations.Detailed error estiination is computed to compare our results witli the existing inethudb.It is shown with the help of tables and figures that the present method is very efficient,has better accuracy and has least computational cost.

关键词： Prey-predator model spectral collocation method Chebyshev, Legendre and Jacobi polynomials error estimation

P-FEMOL ANALYSIS OF PLATE BENDING PROBLEMS

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Acta Mechanica Solida Sinica 1994年第1期7卷 39-45页

作者： Si, Yuan Tsinghua Univ Beijing China

In this paper, the p- version of the finite element method of lines (FEMOL) for the analysis of the Mindlin-Reissner plate bending problems is presented and a class of p-FEMOL elements with polynomial degrees as high as nine is developed. Numerical examples given in this paper show tremendous performance of the present method: namely, rapid convergence rate, high accuracy for both displacements and stress resultants, removal of shear-locking trouble, capability of dealing with difficult problems such as the boundary layer behavior near a free edge and stress concentration around a hole.

关键词： Bending (deformation) Boundary layers Convergence of numerical methods Differential equations Finite element method Geometry Mathematical models Performance Plates (structural components) polynomials Stresses

On Von Neumann’s Inequality for Matrices of Complex polynomials

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American Journal of Computational Mathematics 2021年第4期11卷 289-303页

作者： Joachim Moussounda Mouanda Mathematics Department Blessington Christian University Nkayi Republic of Congo

We prove that every matrix F∈Mk (Pn) is associated with the smallest positive integer d (F)≠1 such that d (F)‖F‖∞ is always bigger than the sum of the operator norms of the Fourier coefficients of F. We establish some inequalities for matrices of complex polynomials. In application, we show that von Neumann’s inequality holds up to the constant 2n for matrices of the algebra Mk (Pn).

关键词： Fourier Coefficients Operator Theory polynomials

NON-INTEGRABILITY AND CHAOS OF A CONSERVATIVE COMPOUND PENDULUM

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Applied Mathematics and Mechanics(English Edition) 1992年第1期13卷 51-59页

作者：凌复华徐如进 Department of Engineering Mechanics Shanghai Jiaotong University

By using a series of canonical transformations (Birkhoff's series), an approximate integral of a conservative compound pendulum is evaluated. Level lines of this approximate integral are compared with the numerical simulation results. It is seen clearly that with a raised energy level, the nearly integrable system becomes non-integrable, i.e. the regular motion pattern changes to the chaotic one. Experiments with such a pendulum device display the behavior mentioned above.

关键词： Chaos theory Integral equations polynomials

ON STABILITY OF SYMPLECTIC ALGORITHMS

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Journal of Computational Mathematics 1995年第1期13卷 64-69页

作者： Li Wang-yao(Computing Centen Academia Sinica, Beijing, China) 中科院计算数学与科学工程计算所北京

The stability of symplectic algorithms is discussed in this paper. There are following conclusions. 1. Symplectic Runge-Kutta methods and symplectic one-step methods with high order derivative are unconditionally critically stable for Hamiltonian systems. Only some of them are A-stable for non-Hamiltonian systems. The criterion of judging A-stability is given. 2. The hopscotch schemes are conditionally critically stable for Hamiltonian systems. Their stability regions are only a segment on the imaginary axis for non-Hamiltonian systems. 3. All linear symplectic multistep methods are conditionally critically stable except the trapezoidal formula which is unconditionally critically stable for Hamiltonian systems. Only the trapezoidal formula is A-stable, and others only have segments on the imaginary axis as their stability regions for non-Hamiltonian systems.

关键词： Method of characteristics Eigenvalues Equation roots Half planes Hopscotch polynomials Coefficients

Efficient numerical treatments for a fractional optimal control nonlinear Tuberculosis model

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International Journal of Biomathematics 2018年第8期11卷 393-423页

作者： N. H. Sweilam S. M. AL-Mekhlafi D. Baleanu Department of Mathematics Faculty of Science Cairo University Giza Egypt Department of Mathematics Faculty of Education Sana a University Sana'a Yemen Department of Mathematics Cankaya University Turkey Institute of Space Sciences Magurele-Bucharest Romania

In this paper, the general nonlinear multi-strain Tuberculosis model is controlled using the merits of Jacobi spectral collocation method. In order to have a variety of accurate results to simulate the reality, a fractional order model of multi-strain Tuberculosis with its control is introduced, where the derivatives are adopted from Caputo's definition. The shifted Jacobi polynomials are used to approximate the optimality system. Subsequently, Newton's iterative method will be used to solve the resultant nonlinear algebraic equations. A comparative study of the values of the objective functional, between both the generalized Euler method and the proposed technique is presented. We can claim that the proposed technique reveals better results when compared to the generalized Euler method.

关键词： Tuberculosis model optimal control problem Jacobi polynomials Caputo derivative generalized Euler method

A numerical study by using the Chebyshev collocation met hod for a problem of biological invasion: Fractional Fisher equation A numerical study by using the Chebyshev collocation met hod for a problem of biological invasion: Fractional Fisher equation

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International Journal of Biomathematics 2018年第8期11卷 71-85页

作者： Mohamed M. Khader Khaled M. Saad Department of Mathematics and Statistics College of Science Al Imam Mohammad Ibn Saud Islamic University (IMSIU) Riyadh Saudi Arabia Department of Mathematics Faculty of Science Benha University Benha Egypt Department of Mathematics College of Arts and Sciences Najran University Najran Saudi Arabia Department of Mathematics Faculty of Applied Science Taiz University Taiz Yemen

In this paper, an efficient numerical method is introduced for solving the fractional (Caputo sense) Fisher equation. We use the spectral collocation method which is based upon Chebyshev approximations. The properties of Chebyshev polynomials of the third kind are used to reduce the proposed problem to a system of ODEs, which is solved by the finite difference method (FDM). Some theorems about the convergence analysis are stated and proved. A numerical simulation is given and the results are compared with the exact solution.

关键词： Fractional Fisher equation FDM Chebyshev polynomials convergence analysis

On non-uniform hyperbolicity assumptions in one-dimensional dynamics

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Science China Mathematics 2010年第7期53卷 1663-1677页

作者： LI HuaiBin SHEN WeiXiao Department of Mathematics University of Science and Technology of ChinaHefei 230026China Department of Mathematics National University of SingaporeSingapore 117543Singapore

We give an essentially equivalent formulation of the backward contracting property,defined by Juan Rivera-Letelier,in terms of expansion along the orbits of critical values,for complex polynomials of degree at least 2 which are at most finitely renormalizable and have only hyperbolic periodic points,as well as all C3 interval maps with non-flat critical points.

关键词： polynomials large derivatives backward contraction interval maps