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

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	Comparative study on order-reduced methods for linear third-order ordinary differential equations
其他题名	Comparative study on order-reduced methods for linear third-order ordinary differential equations
	Ren Zhiru
	2012
发表期刊	FRONTIERS OF MATHEMATICS IN CHINA
ISSN	1673-3452
卷号	7 期号:6 页码:1151-1168
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(x) 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 sinc discretizations 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.
其他摘要	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(x) 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 sinc discretizations 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.
关键词	PRECONDITIONED ITERATIVE METHODS SYSTEMS FLOWS third-order ordinary differential equation order-reduced method sinc discretization preconditioner Krylov subspace method
收录类别	CSCD
语种	英语
资助项目	[State Key Laboratory of Scientific/Engineering Computing, Chinese Academy of Sciences]
CSCD记录号	CSCD:4694324
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/54984
专题	中国科学院数学与系统科学研究院
作者单位	中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Ren Zhiru. Comparative study on order-reduced methods for linear third-order ordinary differential equations[J]. FRONTIERS OF MATHEMATICS IN CHINA,2012,7(6):1151-1168.
APA	Ren Zhiru.(2012).Comparative study on order-reduced methods for linear third-order ordinary differential equations.FRONTIERS OF MATHEMATICS IN CHINA,7(6),1151-1168.
MLA	Ren Zhiru."Comparative study on order-reduced methods for linear third-order ordinary differential equations".FRONTIERS OF MATHEMATICS IN CHINA 7.6(2012):1151-1168.