并构造迭代列，使之收敛于该算子方程之解。
Iterative sequences are also constructed, which converge to the solutions of the operator equation.
分析并提出了微分算子方程形成的数学依据。
This paper analyses and provides the mathematical basis of the forming of differential operational notation and operational notation equation.
本文研究了一类算子方程组的解及边界解的存在性。
In this paper, we study existence of the solutions and boundary solutions for a class of operator equations.
文中采用了几种预条件技术来降低算子方程的条件数。
Several preconditioning techniques have been used to reduce the condition number of the operator equations.
利用算子方程的一些抽象结果来讨论四阶奇异边值问题。
By some abstract results of operator equation, the fourth order singular boundary value problem was discussed.
本文提出了几个新概念，研究了1集压缩型随机算子方程的随机解。
In this paper, we introduce some new concepts, and study random solution of random operator equation of 1 set contractive type.
之后，通过求解一个关键性算子方程，得到此类孤子方程族的换位表。
Then through resolving a key operator equation, we obtain the commutator representation of this hierarchy of the soliton equations.
非饱和土中溶质迁移参数反演问题可以归结为非线性算子方程的求解问题。
Parameter inversion of solute transport inside unsaturated soils was generally solved through a nonlinear operator equation.
分别使用不动点定理，序方法讨论了一类非单调算子方程组解的存在及其迭代。
By using the theory of fixed point and cone theory, we obtain some new results about the system of a monotone operator equations.
构造一个光滑化函数逼近NCP函数，利用光滑化牛顿法求解此非光滑算子方程。
A smoothing function which can be approximated by NCP-function is given and the smoothing Newton method is applied to resolve this nonsmooth operator equation.
由于集值算子在现代数学的广泛应用，本文还研讨了关于集值算子方程解的存在性；
Due to the wide applications of setvalued operators in modern mathematics, the solvability of the setvalued operator equations are studied.
对流一扩散方程中扩散系数反演问题，可以归结为一个特殊的非线性算子方程求解问题。
The problem of determining the diffusive coefficients can be formulated as one of solving a special nonlinear operator equation.
对半正定线性算子方程考虑了一类连续正则化牛顿方法，给出了收敛证明，得到了收敛率。
A convergence proof is given for the continuous analog of the Newton method for linear semi-positive definite operator equations and convergence rates are obtained.
本文讨论了一类非单调的具有分段压缩性质的含参数随机算子方程组的解的存在性和唯一性。
In this paper, the existence and uniqueness theorems of solution of a class Non-monotonic parametric stochastic operator equation with piecewise contraction property is discussed.
通过将问题化为非线性算子方程，推导出算子的形式导数，给出了线性化问题解的等价表达。
By reducing the MREIT problem to a nonlinear operator equation, the formal derivative of the operator and the formula of solution for linearization problem are given.
本文主要研究半序f -型拓扑空间中单调映射的不动点定理和一类非线性算子方程的可解性。
In this paper, we mainly discuss the fixed point theorems of monotone mappings and the solvability of a class of nonlinear operator equations in partially ordered F-type topological Spaces.
利用锥理论和非对称迭代方法，讨论了不具有连续性和紧性条件的增算子方程解的存在唯一性。
By using the cone theory and non-symmetry iteration method, it is studied the existence and uniqueness of solutions of increasing operator equations without continuity and compactness conditions.
提出了1 -集压缩型随机算子方程耦合解的概念，并研究了这类随机算子方程耦合解的存在性。
In this paper, to 1-set contraction random operator equation, the author explained the conception of couple solution, obtained existence theorem of couple solution.
讨论描述希尔伯特空间最终范数连续半群特征的一个算子方程的解，给出这个解的一个显式表达式。
A new perturbation result on the Hilbert space for the eventually norm-continuous semigroups is obtained, which makes the perturbation of the semigroups more abundant.
配置法是以满足纯插值约束条件的方式，寻求算子方程近似解的方法，且具有无需计算数值积分、计算量小、收敛阶高等优点。
The collocation method is a numerical method which search for the approximate solution of the equation by way of meeting pure interpolation condition.
本文利用随机收缩，证明具有随机定义域的非线性随机算子方程组的解的存在与唯一性定理，给出非线性随机积分和微分方程组的某些应用，改进和推广了某些结果。
In this paper, several existence and uniqueness theorems of solutions are proved for the system of nonlinear random operator equations with stochastic domain by using general random contraction.
摘要通过对积分算子谱的估计，作者给出了一阶线性微分差分方程在边值条件下解的存在唯一性定理。
In this paper, by estimates of spectral of an integral operator, the authors give a theorem on the existence of solutions for first order differential difference equations with boundary condition.
该算子具有方程阶数低且能对陡倾角成像的特点，能适应速度场的任意变化。
The operator is characterized by low order equation, imaging for steep dip and adapting for any changes in velocity field.
众所周知，分数次积分算子是调和分析中以偏微分方程为背景的一种重要算子。
It is well-known that fractional integral operator is one of the important operators in harmonic analysis with background of partial differential equations.
在人工调节时间步长法中，通过人为控制方程中算子能量变化的办法调整时间步长；
The first one is the artificial method in adjusting to the time step, which can be realized by controling the variation of operator energy in equation artificially.
文章给出了利用模拟退火算法求解一类扩散方程的参数算子识别反问题的一种新方法。
In this paper, a new approach, which is based on simulated annealing algorithm for solving a class of diffusion equation of parameter operator identification of inverse problem, is presented.
我们研究含非稠定闭线性算子的积-微分方程。
Integro-differential equations with nondensely defined linear operators in Banach space was considered.
通过鞅方法构造耦合算子，研究了多值随机微分方程中的耦合方法。
Through the martingale approach, the construction of coupling operators is explored and coupling methods in multivalued stochastic differential equations are studied.
采用斜向差分算子，建立斜向隐式差分格式，再结合边界条件，对扩散方程进行求解。
Based on the skew direction difference operator, the implicit skew difference schemes were constructed, and the boundary condition was unified, to solve the diffusion equation.
采用斜向差分算子，建立斜向隐式差分格式，再结合边界条件，对扩散方程进行求解。
Based on the skew direction difference operator, the implicit skew difference schemes were constructed, and the boundary condition was unified, to solve the diffusion equation.
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