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基于四次矩阵样条的矩阵微分方程近似解 被引量：1

Approximate solution of matrix differential equations by the quartic matrix spline
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摘要 矩阵微分方程经常出现在物理模型和工程技术模型中。文章给出了用四次矩阵样条构造形如Y′=A(x)Y+B(x),Y(0)=Y0,x∈[a,b],A(x)、B(x)∈C4[a,b]的一阶矩阵线性微分方程初值问题近似解的方法,研究了该方法的逼近误差并编制了实现该方法的一个算法,最后给出一些数值实例;比较结果表明,用四次矩阵样条所构造的近似解的逼近效果要比用三次矩阵样条所构造的近似解的逼近效果好。 Matrix differential equations appear frequently in a wide variety of models in physics and en- gineering. This paper deals with the construction of the approximate solution of first-order matrix lin- ear differential equations given by Y′=A（x）Y＋B（x）,Y（O）=Y0,where x∈[a,b],A（x）、B（x）∈C[a,b], using the quartic matrix spline（QMS）. An estimation of the approximation error and an algorithm for the implementation of the construction method are described. Two illustrative examples are included, and for the same first-order matrix linear differential equation, the results ob- tained by using the QMS are compared with those by using the cubic matrix spline, which shows that the error of approximation by using the QMS is smaller than that by using the cubic matrix soline.
作者 郭清伟 王芳
机构地区 合肥工业大学理学院
出处 《合肥工业大学学报（自然科学版）》 CAS CSCD 北大核心 2007年第11期1537-1541,共5页 Journal of Hefei University of Technology：Natural Science
基金 合肥工业大学基金资助项目(061007F)
关键词 一阶矩阵线性微分方程 三次矩阵样条 四次矩阵样条 逼近 first-order matrix linear differential equation cubic matrix spline quartic matrixspline approximation
分类号 O221.73 [理学—运筹学与控制论]
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参考文献15

  • 1Marzulli P. Global error estimates for the standard parallel shooting method [J]. J Comput Appl Maths, 1991, 34:233--241.
  • 2Rektorys K. The method of discretization in time and partial differential equation[M]. Dordrecht, D Reidel Pub Co, 1982,31--46.
  • 3Boggs P T. The solution of nonlinear system of equations by A-stable integration techniques[J]. SIAM J Numer Anal,1971,8(4):767--787.
  • 4Graham A. Kronecker products and matrix calculus with applications[M]. New York: Wiley, 1981 : 1-- 20.
  • 5Flett T M. Differential analysis[M]. Cambridge, U K: Cambridge University Press, 1980 : 141-- 165.
  • 6Ascher U M, Mattheij R M, Russell R D. Numerical solutions of boundary value problems for ordinary differential equation[M]. New Jersey: Prentice Hall, 1988 : 17-- 48.
  • 7Jodar L, Ponsoda E. Non-autonomous riccati-type matrix differential equations, existence interval, construction of continuous numerical solution and error bounds[J]. IMA J Numer Anal, 1995,15 (1) : 61--74.
  • 8Jodar L,Cortes J C, Morera J L. Construction and computation of variable coefficient Sylvester differential problems [J]. Computers Maths Applic, 1996,32 (8) : 41--50.
  • 9Jodar L, Cortes J C. Rational matrix approximation with a priori error bounds for non-summetrie matrix Rieeati Equations with analytic eoeffieients[J]. IMA J Numer Anal, 1998,18(4) : 545--561.
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同被引文献15

  • 1Marzulli P. Global error estimates for the standard parallel shooting method [J]. J Comput Appl Maths, 1991, 34: 233-241.
  • 2Rektorys K. The method of discretization in time and partial differential equation[M]. Dordrecht: D Reidel Pub Co, 1982: 31-46.
  • 3Boggs P T. The solution of nonlinear system of equations by a stable integration techniques [J]. SIAM J Numer A2 nal ,1971 ,8 (4) :767-787.
  • 4Graham A. Kroneeker product s and matrix calculus with applications[M] . New York :Wiley ,1981 :.
  • 5Flett T M. Differential analysis [M]. Cambridge , U K: Cambridge University Press ,1980:141-165.
  • 6Ascher U M , Mattheij R M , Russell R D. Numerical solutions of boundary value problems for ordinary differential equation[M]. New Jersey : Prentice Hall ,1988:17-48.
  • 7Jodar L , Ponsoda E. Nonautonomous riccatitype matrix differential equations , existence interval , const ruction of continuous numerical solution and error bounds [J]. IMA JNumer Anal ,1995 ,15 (1) :61-74.
  • 8Jodar L , Cortes J C , Morera J L. Const ruction and computation of variable coefficient sylvester differential problems [J]. Computers Maths Applic ,1996 ,32 (8) :41-50.
  • 9Jodar L ,Cortes J C. Rational matrix approximation with a priori error bounds for nonsummetric matrix Riceati Equations with analytic coefficients[J]. IMA J Numer Anal ,1998 ,18 (4) :545-561.
  • 10Jodar L , Ponsoda E. Continuous numerical solutions and error bounds for matrix differential equations[C]// Bainov D , Covachev V. Int Proc First Int Coll Num Anal . VSP Ut rech , The Netherlands ,1993:73-100.

引证文献1

合肥工业大学学报（自然科学版）
2007年 第11期

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