共查询到20条相似文献,搜索用时 218 毫秒
1.
2.
3.
4.
一类高阶多维非线性Schrodinger方程组的有限元分析 总被引:1,自引:0,他引:1
向新民 《高等学校计算数学学报》1984,(1)
的初值问题和周期初值问题,得到了解的存在唯一性。本文讨论这类方程组的周期初值问题的有限元解法,对其半离散Galerkin有限元和全离散格式讨论了收敛阶,最后用Brower不动定理证明了全离散后所得到的非线性方程组的可解性。 相似文献
5.
6.
一类重要的常微分方程源自用线方法求解非线性双曲型 偏微分方程,这类常微分方程的解具有单调性, 因此要求数值方法能保持原系统的这种性质.本文研究多步Runge-Kutta方法求解常微分方程初值问题的保单调性.分别获得了多步Runge-Kutta方法是条件单调和无条件单调的充分条件.
相似文献
7.
本文利用初值问题方法给出了一类二阶线性周期边值问题解的存在唯一性的构造性证明,并利用数值延拓方法,给出了计算实例。因此提供了一种大范围求解这类方程周期解的方法。 相似文献
8.
凸幂凝聚算子的不动点定理及其对抽象半线性发展方程的应用 总被引:4,自引:0,他引:4
从应用问题的需要出发,给出了一类新的算子-凸幂凝聚算子的定义,推广了凝聚算子的概念,并证明了这类新算子的不动点定理,从而推广了著名的Schauder不动点定理和Sadovskii不动点定理.作为应用,获得了Banach空间中一类具有非紧半群的半线性发展方程初值问题整体mild解和正mild解的存在性. 相似文献
9.
将微分方程初值问题转化为等价的积分方程,近来此方法被应用于讨论非线性微分方程初值问题解的存在性.利用凸幂凝聚算子的不动点定理,研究了Banach空间中混合型非线性二阶积分-微分方程的初值问题解的存在性. 相似文献
10.
讨论了刻画层流问题中比重相近的层间相互作用的数学模型的初值问题.通过引进一类函数空间并证明该初值问题的解在所述空间上的一系列先验估计,得到了该初值问题在初值属于Hs(R)(s≥1)时的整体适定性. 相似文献
11.
In practice many problems related to space/time fractional equations depend on fractional parameters. But these fractional parameters are not known a priori in modelling problems. Hence continuity of the solutions with respect to these parameters is important for modelling purposes. In this paper we will study the continuity of the solutions of a class of equations including the Abel equations of the first and second kind, and time fractional diffusion type equations. We consider continuity with respect to the fractional parameters as well as the initial value. 相似文献
12.
讨论一类在部分区域上的奇摄动反应扩散方程初始边值问题,利用算子理论,得到了相应问题解的渐近性态。 相似文献
13.
In this paper, we study a class of nonlinear operator equations with more extensive conditions in ordered Banach spaces. By using the cone theory and Banach contraction mapping principle, the existence and uniqueness of solutions for such equations are investigated without demanding the existence of upper and lower solutions and compactness and continuity conditions. The results in this paper are applied to a class of abstract semilinear evolution equations with noncompact semigroup in Banach spaces and the initial value problems for nonlinear second-order integro-differential equations of mixed type in Banach spaces. The results obtained here improve and generalize many known results. 相似文献
14.
15.
16.
《Nonlinear Analysis: Theory, Methods & Applications》2005,61(8):1363-1382
In this paper, we develop a theorem for the existence of global solutions of an initial value problems for a class of second-order impulsive integro-differential equations of mixed type in a real Banach space. The results obtained are the generalizations and improvements of various recent results. As an application of the theorem, the existence of global solutions of two mixed boundary value problems for two classes of fourth-order impulsive differential equations are established. 相似文献
17.
Lazhar Bougoffa 《Applied Mathematics Letters》2009,22(8):1248-1251
In this paper, the solutions of initial value problems for a class of second-order linear differential equations are obtained in the exact form by writing the equations in the general operator form and finding an inverse differential operator for this general operator form. 相似文献
18.
Robert Kersner 《Journal of Differential Equations》2004,199(1):47-76
We study well-posedness of initial value problems for a class of singular quasilinear parabolic equations in one space dimension. Simple conditions for well-posedness in the space of bounded nonnegative solutions are given, which involve boundedness of solutions of some related linear stationary problems. By a suitable change of unknown, the above results can be applied to classical initial-boundary value problems for parabolic equations with singular coefficients, as the heat equation with inverse square potential. 相似文献
19.
MoJiaqi LinWantao ZhuJiang 《高校应用数学学报(英文版)》2004,19(4):367-373
A class of initial boundary value problems for the reaction diffusion equations are considered. The asymptotic behavior of solution for the problem is obtained using the theory of differential inequality. 相似文献
20.
M. R. Mataušek 《Journal of Optimization Theory and Applications》1976,20(1):37-46
The paper discusses the solution of boundary-value problems for ordinary differential equations by Warner's algorithm. This shooting algorithm requires that only the original system of differential equations is solved once in each iteration, while the initial conditions for a new iteration are evaluated from a matrix equation. Numerical analysis performed shows that the algorithm converges even for very bad starting values of the unknown initial conditions and that the number of iterations is small and weakly dependent on the starting point. Based on this algorithm, a general subroutine can be realized for the solution of a large class of boundary-value problems. 相似文献