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

doi:10.1007/s11464-012-0242-1

Front Math Chin

2012, Vol. 7

Issue (6) : 1151-1168 https://doi.org/10.1007/s11464-012-0242-1

RESEARCH ARTICLE

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

Zhiru REN(

)

State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P. O. Box 2719, Beijing 100190, China

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Abstract

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.

Keywords third-order ordinary differential equation order-reduced method sinc discretization preconditioner Krylov subspace method

Corresponding Author(s): REN Zhiru,Email:renzr@lsec.cc.ac.cn

Issue Date: 01 December 2012

Cite this article:

Zhiru REN. Comparative study on order-reduced methods for linear third-order ordinary differential equations[J]. Front Math Chin, 2012, 7(6): 1151-1168.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-012-0242-1
https://academic.hep.com.cn/fmc/EN/Y2012/V7/I6/1151

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