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Lax方程组的求解公式 总被引:1,自引:0,他引:1
本文给出了一些著名的非线性演化方程的Lax方程组求解公式.利用这些公式,只需算积分就能不断求得这些方程的解.从而提供了利用Lax方程组求解非线性方程的新途径. 相似文献
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由同顺 《高校应用数学学报(A辑)》2016,(4):491-500
使用Arnold等人提出的求解椭圆方程的间断有限元的一般框架及新的处理非线性对流项的方法,得到了非线性对流扩散方程的三层隐-显hp-LDG方法的误差估计.对Burgers方程进行了数值计算,计算结果验证了文中得到的理论结果. 相似文献
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求解NLS+方程暗孤子解的问题早已解决,但其求解过程需要对Jost解的解析性进行繁杂的理论分析.本文用一种简单的方法,把求解NLS+方程暗孤子解的问题归结为纯粹的代数运算. 相似文献
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研究高阶Camassa-Holm方程的行波解,采用一种新的方法求解行波方程,获得了高阶Camassa-Holm方程的一类行波解. 相似文献
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根据Painleve分析的已知结果,给出了KdV方程和Kuperschmidt方程的新的递推求解公式。 相似文献
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RLW—Burgers方程的精确解 总被引:6,自引:0,他引:6
借助未知函数的变换,RLW-Burgers方程和KdV-Burgers方程化为易于求解的齐次形式的方程,从而得到RLW-Burgers方程和KdV-Burgers方程的精确解。 相似文献
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Given a sequence of transition matrices for a nonstationary Markov chain, a matrix whose product on the right of a transition matrix yields the next transition matrix is called a causative matrix. A causative matrix is strongly causative if successive products continue to yield stochastic matrices. This paper presents necessary and sufficient conditions for a matrix to be causative and strongly causative with respect to an invertible transition matrix, by considering the causative matrix as a linear transformation on the rows of the transition matrix. 相似文献
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给定矩阵X和B,利用矩阵的广义奇异值分解,得到了矩阵方程X~HAX=B有Hermite-广义反Hamiton解的充分必要条件及有解时解的—般表达式.用S_E表示此矩阵方程的解集合,证明了S_E中存在唯一的矩阵(?),使得(?)与给定矩阵A的差的Frobenius范数最小,并且给出了矩阵(?)的表达式;同时也证明了S_E中存在唯一的矩阵A_o,使得A_o是此矩阵方程的极小Frobenius范数Hermite-广义反Hamilton解,并且给出了矩阵A_o的表达式. 相似文献
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S.M Roberts 《Journal of Mathematical Analysis and Applications》1984,104(1):173-188
The choice of partitioning the system matrix for a system of N linear ordinary differential equations may determine the ease or difficulty of obtaining a solution by the invariant imbedding method of Scott. This paper shows how the configuration and partitioning of the system matrix is reflected in the fundamental matrix. The partitioning of the fundamental matrix is the key to the ease or difficulty of obtaining a solution. If the fundamental matrix is known for a given system matrix configuration and partitioning, then the fundamental matrix associated with a new system matrix configuration may be derived by the same row and column interchanges that transformed the old system matrix into the new system matrix. The fundamental matrix for the new system matrix does not have to be recalculated anew from the Kronecker delta initial conditions. 相似文献
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广义严格对角占优阵的判定程序 总被引:3,自引:1,他引:2
陈神灿 《高等学校计算数学学报》1997,19(4):324-329
1 引言和符号 在本文中,均采用下列符号而不再重申.恒用N表示前n个自然数的集合;而用Mn(C)和Mn(R)分别表示所有n阶复矩阵和所有n阶实矩阵的集合. Z_N={A|A=(a_(ij))_(n×n)∈Mn(R),a_(ij)≤0,i,j∈N,i≠j},I恒表示单位矩阵. 如果A∈Mn(R)且A的所有元素都为非负实数,则称A为非负方阵,并记为A≥0;若A的所有元素都为正数,则称A为正矩阵,并记为A>0. 对A=(a_(ij))(n×n)∈Mn(C),令A_i(A)=sum from j=1 j≠i to n (|a_(ij)|(i=1、2…… n)) ;若把A的非零元用1代替 而得到—个n阶(0,1)矩阵。称为A的导出矩阵。记为;而把A的比较矩阵记为 u(A)=(b_(ij))_(n×n))其中b_(ij)=|a_(ij)|,b_(ij)=-|a_(ij)|(i,j∈N i≠j) 相似文献
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We introduce and study matrix Christoffel functions for a matrix
weight W.
We find an explicit expression of the matrix Christoffel functions
in terms of any sequence of orthonormal matrix polynomials with
respect to W. An extremal property related to the matrix moment
problem defined by W is established for the matrix Christoffel
functions. We finally find the relative asymptotic behavior of
the matrix Christoffel functions associated to matrix weights in
the matrix Nevai class. 相似文献
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The effects of Poisson contraction on matrix cracking in unidirectional fiber-reinforced brittle-matrix composites are studied in this paper. The fibers, initially held in the matrix by a compressive pressure due to the thermal expansion mismatch, are subjected to frictional slipping over the matrix as soon as a fiber-bridged crack is formed. The friction between the fibers and the matrix is assumed to follow the Coulomb friction law. A shear-lag model, which includes the Poisson contraction and the friction due to the relative fiber/matrix slipping, is adopted to calculate the stress and strain fields in the fibers and matrix. Using the energy balance approach, a relation for the critical matrix cracking stress for propagating of a semi-infinite fiber-bridged crack is derived. The results obtained show that the Poisson contraction has a strong effect on the predicted matrix cracking stress in brittle-matrix composites, especially in composites with a stiff matrix. 相似文献
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ON HERMITE MATRIX POLYNOMIALS AND HERMITE MATRIX FUNCTIONS 总被引:1,自引:0,他引:1
In this paper properties of Hermite matrix polynomials and Hermite matrix functions are studied. The concept ot total set with respect to a matrix functional is introduced and the total property of the Hermite matrix polynomials is proved. Asymptotic behaviour of Hermite matrix polynomials is studied and the relationship of Hermite matrix functions with certain matrix differential equations is developed. A new expression of the matrix exponential for a wide class of matrices in terms of Hermite matrix polynomials is proposed. 相似文献