共查询到19条相似文献,搜索用时 140 毫秒
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李文献 《数学物理学报(A辑)》1989,9(1):75-89
本文的主要结果是:提出了一个2m维向量函数的散射系统,当m=1时,这系统就是AKNS系统;研究了该系统的散射和逆散射问题,导出其相应的Gel'fand-Levitan-Marchenko积分方程和逆问题解的表达式。 相似文献
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谢大来 《纯粹数学与应用数学》1992,8(2):117-124
本文研究以下两类非线性微分方程组零解的稳定性:■我们用定性方法,从分析轨线在原点邻域中的性态出发,得到了零解渐近稳定和不稳定的相应定理,可通过查表加以判定,简捷、实用。另外还可根据定理的条件具体构造渐近稳定和不稳定的系统。 相似文献
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提出几类扩大的积分微分方程组,利用函数迭代法及变上限函数的求导法则,证明其可积性,得出相应的求解公式. 相似文献
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二阶线性微分方程组解法研究 总被引:1,自引:0,他引:1
采用降阶法和欧拉方法对一类二阶线性微分方程组的求解进行了研究,并给出了当系数矩阵的特征根为三种不同情况(互异、共轭、二重根)时微分方程组的通解公式,并通过算例验证了通解的正确性. 相似文献
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We discuss the possibility of applying linear structures for solving nonlinear differential equations. 相似文献
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This paper presents a strong predictor-corrector method for the numerical solution of stochastic delay differential equations (SDDEs) of Itô-type. The method is proved to be mean-square convergent of order min{$1/2, \hat{p}$} under the Lipschitz condition and the linear growth condition, where $\hat{p}$ is the exponent of Hölder condition of the initial function. Stability criteria for this type of method are derived. It is shown that for certain choices of the flexible parameter $p$ the derived method can have a better stability property than more commonly used numerical methods. That is, for some $p$, the asymptotic MS-stability bound of the method will be much larger than that of the Euler-Maruyama method. Numerical results are reported confirming convergence properties and comparing stability properties of methods with different parameters $p$. Finally, the vectorised simulation is discussed and it is shown that this implementation is much more efficient. 相似文献
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偏微分方程求解中级数思想的体现 总被引:1,自引:0,他引:1
王远弟 《数学的实践与认识》2008,38(1):148-154
旨在介绍级数方法在偏微分方程求解中的应用,体现级数方法自身的特点,特别在波动方程、热传导方程和 Laplace 方程的求解上.这里还通过举例来将其应用于非线性方程初值问题的求解. 相似文献
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We consider the solution of delay differential equations (DDEs) by using boundary value methods (BVMs). These methods require the solution of one or more nonsymmetric, large and sparse linear systems. The GMRES method with the Strang-type block-circulant preconditioner is proposed for solving these linear systems. We show that if a P
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2-stable BVM is used for solving an m-by-m system of DDEs, then our preconditioner is invertible and all the eigenvalues of the preconditioned system are clustered around 1. It follows that when the GMRES method is applied to solving the preconditioned systems, the method may converge fast. Numerical results are given to illustrate the effectiveness of our methods. 相似文献
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INTENSE (INTElligent Nonlinear Systems of Equations solver) is a problem-solving environment that provides necessary computational facilities for finding numerical solutions of ordinary differential equations and systems of nonlinear algebraic equations. INTENSE offers facilities such as a user-friendly interface for specification of problems, an automatic detection of the properties of a problem, a user-friendly interface for specification of a method, an automatic detection of the properties of methods, a mechanism that matches the properties of problems with the properties of methods, the application of a numerical method and supervision of the errors, some lists or graphics of the values of approximate solutions, and solving the problem without specification of a particular method. Bibliography: 35 titles. 相似文献
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针对反问题中出现的第一类算子方程Au=f,其中A是实Hilbert空间H上的一个无界线性算子利用动力系统方法和正则化方法,求解上述问题的正则化问题的解:u'(t)=-A~*(Au(t)-f)利用线性算子半群理论可以得到上述正则化问题的解的半群表示,并证明了当t→∞时,所得的正则化解收敛于原问题的解. 相似文献
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Golikov A. I. Evtushenko Yu. G. Kaporin I. E. 《Computational Mathematics and Mathematical Physics》2019,59(12):2017-2032
Computational Mathematics and Mathematical Physics - A Newton-type method is proposed for numerical minimization of convex piecewise quadratic functions, and its convergence is analyzed.... 相似文献
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