ILL-CONDITIONED MATRICES AND THE INTEGRATION OF STIFF ODES

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:48

Article

SHAMPINE, LF

关键词: STIFF, ORDINARY DIFFERENTIAL EQUATIONS;    BACKWARD DIFFERENTIATION FORMULAS;    ROSENBROCK METHODS;    EXTRAPOLATION;    SEMIIMPLICIT;   

DOI  :  10.1016/0377-0427(93)90025-7

来源: Elsevier

【 摘 要 】

Popular methods for the integration of a stiff initial-value problem for a system of ordinary differential equations (ODEs) require the solution of systems of linear equations. It is shown that the matrices are very ill-conditioned. Implicit linear multistep methods (LMMs) can be evaluated accurately by iteration, even when the matrices are very ill-conditioned. Although semi-implicit methods do not involve iteration, it is observed that codes based on these methods cope with ill-conditioned matrices about as well as codes based on LMMs. An explanation is provided for this fact.

【 授权许可】

Free