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Numerical Stability and Oscillations of Runge-Kutta Methods for Differential Equations with Piecewise Constant Arguments of Advanced Type

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Communications in mathematical Research 2013年第2期29卷 131-142页

作者： Wang Qi ma fu-ming School of Applied mathematics Guangdong University of Technology

For differential equations with piecewise constant arguments of advanced type, numerical stability and oscillations of Runge-Kutta methods are investigated. The necessary and sufficient conditions under which the numerical stability region contains the analytic stability region are given. The conditions of oscillations for the Runge-Kutta methods are obtained also. We prove that the Runge-Kutta methods preserve the oscillations of the analytic solution. Moreover, the relationship between stability and oscillations is discussed. Several numerical examples which confirm the results of our analysis are presented.

关键词： numerical solution Runge-Kutta method asymptotic stability oscillation

A hybrid method for inverse cavity scattering problem for shape

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Applied mathematics(A Journal of Chinese Universities) 2010年第2期25卷 127-136页

作者： LIU Juan ma fu-ming School of mathematics, Jilin University, Changchun 130012, China. School of mathematics Jilin University Changchun China

In this paper, we give a hybrid method to numerically solve the inverse open cavity scattering problem for cavity shape, given the scattered solution on the opening of the cavity. This method is a hybrid between an iterative method and an integral equations method for solving the Cauchy problem. The idea of this hybrid method is simple, the operation is easy, and the computation cost is small. Numerical experiments show the feasibility of this method, even for cases with noise.

关键词： Open cavity Cauchy problem Helmholtz equation integral equations system method iterativehybrid method.

Dynamics and Long Time Convergence of the Extended Fisher-Kolmogorov Equation under Numerical Discretization

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Communications in mathematical Research 2013年第1期29卷 51-60页

作者： Wang Jue ma fu-ming College of Science Harbin Engineering University

We present a numerical study of the long time behavior of approxima- tion solution to the Extended Fisher-Kolmogorov equation with periodic boundary conditions. The unique solvability of numerical solution is shown. It is proved that there exists a global attractor of the discrete dynamical system. furthermore, we obtain the long-time stability and convergence of the difference scheme and the upper semicontinuity d（Ah,τ, .A） → O. Our results show that the difference scheme can effectively simulate the infinite dimensional dynamical systems.

关键词： Extended Fisher Kolmogorov equation finite difference method global attractor long time stability and convergence

Variational Approach to Scattering by Inhomogeneous Layers Above Rough Surfaces

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Communications in mathematical Research 2014年第1期30卷 71-80页

作者： LUAN TIAN ma fu-ming College of mathematics Jilin University College of mathematics Beihua University

In this paper, we study, via variational methods, the problem of scattering of time harmonic acoustic waves by unbounded inhomogeneous layers above a sound soft rough surface. We first propose a variational formulation and exploit it as a theoretical tool to prove the well-posedness of this problem when the media is non-absorbing for arbitrary wave number and obtain an estimate about the solution, which exhibit explicitly dependence of bound on the wave number and on the geometry of the domain. Then, based on the non-absorbing results, we show that the variational problem remains uniquely solvable when the layer is absorbing by means of a priori estimate of the solution. Finally, we consider the finite element approximation of the problem and give an error estimate.

关键词： Helmholtz equation rough surface scattering problem

The Factorization Method to Solve a Class of Inverse Potential Scattering Problems for Schrdinger Equations

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Communications in mathematical Research 2010年第4期26卷 321-336页

作者： LI YUAN ma fu-ming School of mathematics Jilin University Changchun 130012 School of mathematics Heilongjiang University Harbin150080

This paper is concerned with the inverse scattering problems for Schrdinger equations with compactly supported *** purpose of reconstructing the support of the potential,we derive a factorization of the scattering amplitude operator A and prove that the ranges of （A＊ A） ^1/4 and G which maps more general incident fields than plane waves into the scattering amplitude *** an application we characterize the support of the potential using only the spectral data of the operator A.

关键词： factorization method inverse scattering Schrdinger equation interior transmission problem

An Improved Hybrid Method for Inverse Obstacle Scattering Problems

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Communications in mathematical Research 2011年第3期27卷 215-226页

作者： LIU JUAN ma fu-ming College of Information Science and Technology Jinan University Guangzhou 510632 School of mathematics Jilin University Changehun 130012

An improved hybrid method is introduced in this paper as a numerical method to reconstruct the scatterer by far-field pattern for just one incident direction with unknown physical properties of the scatterer. The improved hybrid method inherits the idea of the hybrid method by Kress and Serranho which is a combination of Newton and decomposition method, and it improves the hybrid method by introducing a general boundary condition. The numerical experiments show the feasibility of this method.

关键词： hybrid method inverse obstacle scattering one incident direction unknown scatterer

A PML Method for Electromagnetic Scattering from Two-dimensional Overfilled Cavities

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Communications in mathematical Research 2009年第1期25卷 53-68页

作者： Liu JUAN ma fu-ming College of mathematics Jilin University Changchun 130012

In this paper, we consider electromagnetic scattering problems for two-dimensional overfilled cavities. A half ringy absorbing perfectly matched layer （PML） is introduced to enclose the cavity, and the PML formulations for both TM and TE polarizations are presented. Existence, uniqueness and convergence of the PML solutions are considered. Numerical experiments demonstrate that the PML method is efficient and accurate for solving cavity scattering problems.

关键词： overfilled cavity scattering TM polarization TE polarization perfectly matched layer (PML) DtN operator

A Split Least-squares Characteristic Procedure for Convection-dominated Parabolic Integro-differential Equations

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Communications in mathematical Research 2015年第1期31卷 1-14页

作者： GUO HUI fu HONG-FEI ma fu-ming College of Science China University of Petroleum

In this paper, we combine a split least-squares procedure with the method of characteristics to treat convection-dominated parabolic integro-differential equations. By selecting the least-squares functional properly, the procedure can be split into two independent sub-procedures, one of which is for the primitive unknown and the other is for the flux. Choosing projections carefully, we get optimal order H^1 （Ω） and L^2（Ω） norm error estimates for u and sub-optimal （L^2（Ω））^d norm error estimate for σ. Numerical results are presented to substantiate the validity of the theoretical results.

关键词： split least-square characteristic convection-dominated convergence analysis

An Algorithm for Cavity Reconstruction in Electrical Impedance Tomography

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Communications in mathematical Research 2011年第3期27卷 279-288页

作者： FENG TIAN-HONG ma fu-ming School of mathematics Jilin University Changchun 130012

We consider the inverse problem of finding cavities within some object from electrostatic measurements on the boundary. By a cavity we understand any object with a different electrical conductivity from the background material of the body. We give an algorithm for solving this inverse problem based on the output nonlinear least-square formulation and the regularized Newton-type iteration. In particular, we present a number of numerical results to highlight the potential and the limitations of this method.

关键词： electrical impedance tomography conductivity Levenberg-marquardt (L-M) algorithm