数理方程近似求解的数论方法

本文,我们用数论网格．．．建议了一个求解数学物理方程的近似方法,此处Ｆｎ表示Ｆｉｂｏｎａｃｃｉ贯。若初始函数适当光滑,本文将给出误差估计,两个例子都表明这一方法优于经典网格方法。     

热传导方程的小波解法

本文利用微分算子的小波表示,讨论一维热传导方程初值问题的Daubechies小波解,给出此问题的显式离散格式。由于小波在时间和频率上的局部性,此方法特别适用于有奇异解的热传导方程,逼近精度高,而且没有发生解的振荡现象。     

移动边界半线性热传导方程始边值问题分析近似解

本文应用Fourier方法求得移动边界非齐次线性热传导方程始边值问题解及半线性方程问题分析近似解     

热传导方程的一类半无界问题

本文推广了对称开拓法，解决了热传导方程的在有限端具有比较广泛的一类边值条件的半无界问题，并求出解的表示式。     

Reissner-Mindlin板问题的一种有限元近似解

通过应用对板的厚度做局部修改的混合有限元方法,计算R e issner-M ind lin板问题的近似解,得到横向位移和旋度的误差分别在H1模和L2模意义下的阶都是2,并且它们不依赖于板的厚度.     

论双曲型方程初一边值问题和初值问题解法的统一性

作者探索把双曲型方程初一边值问题中的初始函数在相应的本征函数族下展开成为Fourier级数，把初始函数延拓到整个空间，把初一边值问题转化成为初值问题，从而使这两类不同的定解问题的解法统一起来。     

轴对称渗流中自由边界问题的近似解法

１．问题的提法 本文讨论各向异性非均匀介质的轴对称稳定渗流问题,我们延用［７］的记号。设有一水井（或油井）,其截面如图１所示,ｚ轴为对称轴,Ｄ为渗流区域,其边界为ＡＢＣＥＦＡ,Ｋ＝｛ｋｉｊ（ｒ,ｚ,ｈ,ｑ）｝为对称渗流张量,它依赖于柱坐标中的ｒ,ｚ,压头ｈ＝ｚ＋ｐ／ρｇ及渗流速率其中ｐ为点（ｒ,ｚ）处的压力,ρ为流体密度,ｇ为重力加速度．ｒ０为井的半径,Ｈ１为液面的高度,同时假设当ｒ≥Ｒ时,其渗流速度Ｖ＝０． 由渗流理论,有引入热函数,流函数 Ｄ中一点）,则满足下列一阶非线性方程组其中,若（ｉ＝ １…     

一类奇异积分方程组的样条间接近似解法

本文利用三次复插值样条函数给了定义于复平面上光滑封闭曲线上的一类奇异积分方程组（１）的一种间接近似解法，讨论了误差估计和一致收敛性。     

求方程近似解的三种方法

我们知道,在许多实际问题中,经常会遇到超越方程、高次代数方程或其他类型的方程．要想求得这类方程的精确值,几乎是不可能的,因此需要寻求方程的近似解．对于求方程近似解的方法,吴老师给同学们上了一次这样的习题课：首先,她出了一道题：如图1所示,设有一半径为R的半圆,试过原点O做一直线L,将半圆面积二等分,求L的倾角a,要求精确到小数点第二位．同学们经过思考后,认为应根据问题的要求建立关于a的方程,他们采用了两种比较简单的方法．－（1）利用初等数学知识,如图12）利用定积分知识：,均可得到方程（其中x=2a）接着,…     

一阶线性隐式微分算子方程的近似解

本文采用投影法讨论了Hilbert空间中一阶线性隐式微分算子方程的Cauchy问题的近似解的收敛性及误差估计.     

约束非线性l_1问题的光滑近似算法

针对约束非线性l_1问题不可微的特点,提出了一种光滑近似算法.该方法利用" "函数的光滑近似函数和罚函数技术将非线性l_1问题转化为无约束可微问题,并在适当的假设下,该算法是全局收敛的.初步的数值试验表明算法的有效性.     

Cauchy Problem for Semilinear Wave Equations in Four Space Dimensions with Small Initial Data

In this paper, we consider the Cauchy problem ◻u(t,x) = |u(t,x)|^p, (t,x) ∈ R^+ × R^4 t = 0 : u = φ(x), u_t = ψ(x), x ∈ R^4 where ◻ = ∂²_t - Σ^4_{i=1}∂²_x_i, is the wave operator, φ, ψ ∈ C^∞_0 (R^4). We prove that for p > 2 the problem has a global solution provided tile initial data is sufficiently small.     

The Cauchy Problem of the Porous Medium Equation with Absorption

In this paper we study the existence of solution for the following Cauchy problem {u_t = Δu^m - u^p u(x,0) = u_0(x) We show how the growth condition of initial trace is determined by the absorption.     

Fourier Moment Method with Regularization for the Cauchy Problem of Helmholtz Equation

In this paper, we consider the reconstruction of the wave field in abounded domain. By choosing a special family of functions, the Cauchy problemcan be transformed into a Fourier moment problem. This problem is ill-posed. Wepropose a regularization method for obtaining an approximate solution to the wavefield on the unspecified boundary. We also give the convergence analysis and errorestimate of the numerical algorithm. Finally, we present some numerical examples toshow the effectiveness of this method.     

Global Existence of Solutions for the Cauchy Problem of the Kawahara Equation with L 2 Initial Data

In this paper we study solvability of the Cauchy problem of the Kawahara equation 偏导dtu ＋ au偏导dzu ＋ β偏导d^3xu ＋γ偏导d^5xu = 0 with L^2 initial data. By working on the Bourgain space X^r,s（R^2） associated with this equation, we prove that the Cauchy problem of the Kawahara equation is locally solvable if initial data belong to H^r（R） and -1 〈 r ≤ 0. This result combined with the energy conservation law of the Kawahara equation yields that global solutions exist if initial data belong to L^2（R）.     

The approximating behavior on nonlinearities of solutions of a degenerate parabolic equation

The approximating character of solutions of a degenerate parabolicequation is studied in this paper. We will show that the solutionsare Lipschitz continuous with respect to the nonlinearitiesof the equations. An explicitly approximating estimate is obtained.     

The Perturbation of the Interface of the Two-dimensional Diffraction Problem and an Approximating Muskat Modal

ln this paper, a new transformation is found out to straighten the interface Γ_2 x = f(y), f ∈ C^{2+a}([0, a]), f_y|_y =0, δ < f < l-δ,δ > 0,δ,l=constants and a perturbation of the interface is considered for a two dimensional diffraction problem. And the existence, uniqueness and regularity of an appeoximating Muskat model are proved.     

A Fourth-Order Modified Method for the Cauchy Problem of the Modified Helmholtz Equation

This paper is concerned with the Cauchy problem for the modified Helmholtz equation in an infinite strip domain 0 < x≤ 1, y ∈ R. The Cauchy data at x = 0 is given and the solution is then sought for the interval 0 < x ≤1. This problem is highly ill-posed and the solution (if it exists) does not depend continuously on the given data. In this paper, we propose a fourth-order modified method to solve the Cauchy problem. Convergence estimates are presented under the suitable choices of regularization parameters and the a priori assumption on the bounds of the exact solution. Numerical implementation is considered and the numerical examples show that our proposed method is effective and stable.     

反向热传导问题的一种新的正则化方法

讨论一个高维反向热传导问题,这是一个经典的严重不适定问题.关于这一问题我们给出一种新的正则化方法-改进的Tikhonov正则化方法,以恢复解对数据的连续依赖性.通过构造一个重要的不等式和提高先验光滑条件,获得正则解在0相似文献