柱形域椭圆型偏微分方程的横向本征函数的解法  

ON THE TRANSVERSE EIGENVECTOR SOLUTION OF THE ELLIPTIC PARTIAL DIFFERENTIAL EQUATION IN THE PRISMATIC DOMAIN

作　　者：钟万勰[1] 钟翔翔 

机构地区：[1]大连理工大学 [2]纽约州立大学

出　　处：《数值计算与计算机应用》1992年第2期107-118,共12页Journal on Numerical Methods and Computer Applications

摘　　要：一、引 论核柱形结构在工程中是常见的,它的求解方法有很大的实际意义也很有理论价值。The algebraic Riccati equations are derived by the limiting process of the semi-analyticalmethod reduced transversely discretized model of the partial differential equation via the va-riational principle. The close relation of that model with the equations in the linear quadraticoptimal control is pointed out. The dual vector is introduced and the physical interpretationfor the positive definite matrix solution of the Riccati equations is given on that basis. Thecanonical transformation matrix is constructed with the solution of the algebraic Riccati equa-tions, then the Hamiltonian matrix is block-diagonalized and the size of the eigenvalue equa-tion is reduced to half of the original one. It is only necessary to solve one of the two equations,the other one can be obtained by some elementary matrix algebraic operations. That gives thefoundation for the eigenvector expansion method in solving differential equations.

关 键 词：偏微分方程 本征函数 椭圆型 解法 

分 类 号：O241.82[理学—计算数学]