Frontiers of Mathematics in China >
Comparative study on order-reduced methods for linear third-order ordinary differential equations
Received date: 08 Mar 2012
Accepted date: 16 Sep 2012
Published date: 01 Dec 2012
Copyright
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.
Zhiru REN . Comparative study on order-reduced methods for linear third-order ordinary differential equations[J]. Frontiers of Mathematics in China, 2012 , 7(6) : 1151 -1168 . DOI: 10.1007/s11464-012-0242-1
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