Comparative study on order-reduced methods for linear third-order ordinary differential equations

作     者：Zhiru REN 

作者机构：State Key Laboratory of Scientific/Engineering Computing Institute of ComputationalMathematics and Scientific/Engineering Computing Academy of Mathematics andSystems Science Chinese Academy of Sciences P. O. Box 2719 Beijing 100190 China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2012年第7卷第6期

页      面：1151-1168页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the State Key Laboratory of Scientific/ Engineering Computing  Chinese Academy of Sciences 

主　　题：third-order ordinary differential equation order-reduced method sine discretization preeonditioner Krylov subspace method 

摘      要：The linear third-order ordinary differential equation （ODE） can be transformed into a system of two second-order ODEs by introducing a variable replacement, which is different from the common order-reduced approach. We choose the functions p（z） and q（x） in the variable replacement to get different cases of the special order-reduced system for the linear third-order ODE. We analyze the numerical behavior and algebraic properties of the systems of linear equations resulting from the sine diseretizations of these special second-order ODE systems. Then the block-diagonal preconditioner is used to accelerate the convergence of the Krylov subspace iteration methods for solving the discretized system of linear equation. Numerical results show that these order-reduced methods are effective for solving the linear third-order ODEs.