Krylov precise time-step integration method. (English) Zbl 1130.65070

Fung, T. C.; Chen, Z. L.

Int. J. Numer. Methods Eng. 68, No. 11, 1115-1136 (2006).

Summary: An efficient precise time-step integration (PTI) algorithm to solve large-scale transient problems is presented in this paper. The Krylov subspace method and the Padé approximations are applied to modify the original PTI algorithm in order to improve the computational efficiency. Both the stability and accuracy characteristics of the resultant algorithms are investigated. The efficiency can be further improved by expanding the dimension to avoid the computation of the particular solutions. The present algorithm can also be extended to tackle nonlinear problems without difficulty. Two numerical examples are given to illustrate the highly accurate and efficient algorithm.

MSC:

65L05	Numerical methods for initial value problems involving ordinary differential equations
34A30	Linear ordinary differential equations and systems
65F10	Iterative numerical methods for linear systems

Keywords:

precise time-step integration (PTI) algorithm; Krylov subspace method; Padé approximations; Arnoldi algorithm; stability; numerical examples

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