A TAILORED FINITE POINT METHOD FOR THE HELMHOLTZ EQUATION WITH HIGH WAVE NUMBERS IN HETEROGENEOUS MEDIUM

In this paper, we propose a tailored-finite-point method for the numerical simulation of the Helmholtz equation with high wave numbers in heterogeneous medium. Our finite point method has been tailored to some particular properties of the problem, which allows us to obtain approximate solutions with the same behaviors as that of the exact solution very naturally. Especially, when the coefficients are piecewise constant, we can get the exact solution with only one point in each subdomain. Our finite-point method has uniformly convergent rate with respect to wave number k in L^2-norm.     

GLOBAL NONEXISTENCE FOR A VISCOELASTIC WAVE EQUATION WITH ACOUSTIC BOUNDARY CONDITIONS

This paper deals with a class of nonlinear viscoelastic wave equation with damping and source terms ■ with acoustic boundary conditions. Under some appropriate assumption on relaxation function g and the initial data, we prove that the solution blows up in finite time if the positive initial energy satisfies a suitable condition.     

AN ASYMPTOTIC SOLUTION OF THE NONLINEAR REDUCED WAVE EQUATION

1 IntroductionIn the theory of nonlinear optics[1], one is led to consider a nonlinear reduced wave equationwhere k is the wave number and n = n'(IuI') is a function of intensity Of the field and is calledthe index of refraction.We consider the case when the optical beam propagates in a quadratic index nledia sothat n'(luI') can be written aswhere no and n1 are constants.With IuI = O(k--'), d > 0, and following the discussion of this equation in two dimensionalspace (see [2]), we writeSubst…     

声波方程吸收边界条件的稳定性分析

引言对于无界区域中波动现象的数值模拟，必需引进人工边界将计算限制在一个有界区域上．为了确定解，需要在人工边界上加适当的边界条件．对于声波和弹性波方程，这样的一组人工边界条件，也叫吸收边界条件，在［1，2］中被系统地构造出来．对于声波方程，这些吸收边界条件恰好是单程波方程的近似．如山中所指出，减少边界反射，便于在计算中应用和稳定性是构造吸收边界条件的三点关键．Ellgqllist和Maid。用模态分析方法15］证明，带有［IJ中构造的吸收边界条件的波动方程初边值问题是适定的，并且估计了人工边界所产生的误差．对于更广…     

EXISTENCE AND UNIQUENESS OF BV SOLUTIONS FOR THE POROUS MEDIUM EQUATION WITH DIRAC MEASURE AS SOURCES

The aim of this paper is to discuss the existence and uniqueness ofsolutions for the porous medium equation ut-(u^m)xx=μ（x） in （x,t）∈R×（0,+∞） with initial condition u(x,0)=u0(x) x∈（-∞,+∞）,where μ(x) is a nonnegative finite Radon measure, u0∈L^1 (R)∩L^∞ (R) is a nonnegative function, and m>1, and R≡(-∞, +∞).     

关于调和方程自然积分算子的一个定理

关于调和方程自然积分算子的一个定理冯康，余德浩（中国科学院计算中心）ＡＴＨＥＯＲＥＭＦＯＲＴＨＥＮＡＴＵＲＡＬＩＮＴＥＧＲＡＬＯＰＥＲＡＴＯＲＯＦＨＡＲＭＯＮＩＣＥＱＵＡＴＩＯＮ￥ＦｅｎｇＫａｎｇ；ＹｕＤｅ－ｈａｏ（ＣｏｍｐｕｔｉｎｇＣｅｎｔｅｒ，Ａ...     

带吸收边界条件的声波方程显式差分格式的稳定性分析

１．引言 在进行无界或半无界区域上各种波动方程的数值求解时,需引进入工边界以限制计算范围,在这些边界上应加相应的人工边界条件．这种边界条件应保证所求得的有界区域上的解很好地逼近原来无界区域上的解．对波动方程来说,就是在边界上人工反射应尽可能地小,使之对区域内部解的影响在允许的误差范围以内.因而它们被称为无反射边界条件或吸收边界条件．这种边界条件还应保证所形成的有界区域上的微分方程定解问题是适定的．这也是各种数值方法稳定的必要条件。 近二十多年来,已发展了声波方程的各种类型的吸收边界条件,其中以Ｃｌ…     

利用正则化方法求解浅海声波散射问题

讨论了浅海中波导的声波散射问题，我们将该问题归结为一个第一类边界积分方程，利用正同化方法求解，并证明了该方法的收敛性，数值例子表明了该方法的简单与有效性。     

GUARANTEED BOUNDS FOR THE SOLUTION OF THE WAVE EQUATION

Abstract

Numerical solution of the wave equation in the form of close lower and upper bounds provides a secure a posteriori error estimate that can be used for efficient accuracy control. The method considered in this paper uses some monotone properties of the differential operator in the wave equation to construct bounds for the solution in the form of trigonometric polynomials of x. Aspects of the numerical implementation, the accuracy of the computed bounds and some numerical examples are discussed.     

THE UNIQUENESS OF SOLUTION FOR A KIND OF NONLINEAR IMPULSIVE INTEGRODIFFERENTIAL EQUATION

In this paper, we discuss the uniqueness of solutions for a kind of impulsive differential equations, and obtain the successive sequence of solution and the error estimate of convergence rate.     

GLOBAL UNIQUENESS IN THE INVERSE ACOUSTIC SCATTERING PROBLEM WITHIN POLYGONAL OBSTACLES

§1. Introduction √ Let k ∈R, λ> 0 and i = ?1. We consider an acoustic scattering problem by animpenetrable obstacle D ? R2: ?u k2u = 0, in R2 \ D, …     

A PICARD-TYPE THEOREM AND A UNIQUENESS THEOREM OF NON-ARCHIMEDEAN ANALYTIC CURVES IN PROJECTIVE SPACE

In this article, we prove a Picard-type Theorem and a uniqueness theorem for non-Archimedean analytic curves in the projective space P~n(F), where the characteristic of F is 0 or positive. In the main results of this article, we ignore the zeros with large multiplicities.