Estimation of longest stability interval for a kind of explicit linear multistep methods. (English) Zbl 1204.65093
Summary: New explicit linear three-order four-step methods with longest interval of absolute stability are proposed. Some numerical experiments are made for comparing different kinds of linear multistep methods. It is shown that the stability intervals of the proposed methods can be longer than that of known explicit linear multistep methods.
MSC:
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
Keywords:
linear three-order four-step methods; interval of absolute stability; numerical experiments; linear multistep methodsReferences:
| [1] | Springer Series in Computational Mathematics 14 pp xvi+601– (1991) |
| [2] | pp x+293– (1991) |
| [3] | (1883) |
| [4] | DOI: 10.1016/S0377-0427(00)00455-6 · Zbl 0969.65063 · doi:10.1016/S0377-0427(00)00455-6 |
| [5] | 3 pp 27– (1963) |
| [6] | DOI: 10.1007/BF01396187 · Zbl 0457.65054 · doi:10.1007/BF01396187 |
| [7] | Mathematica Numerica Sinica 8 (3) pp 299– (1986) |
| [8] | pp xv+278– (1973) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
