论文信息 - Stiffly Stable Linear Multistep Methods of Extended Order

Stiffly Stable Linear Multistep Methods of Extended Order

Certain linear k-step methods of order k (the Gear formulas) have proven very useful in the integration of stiff equations, but are of sixth order or less. In this paper, we investigate the stiff stability property of k-step methods of order $m < k$, and derive particular methods of this kind which can be viewed as extensions of the Gear formulas, and include formulas of order greater than six.

J. M. Varah

[1] Miloš Zlámal. Finite element multistep discretizations of parabolic boundary value problems , 1975 .

[2] C. W. Gear,et al. The automatic integration of stiff ordinary differential equations , 1968, IFIP Congress.

[3] M. Marden. Geometry of Polynomials , 1970 .

[4] J. Lambert. Computational Methods in Ordinary Differential Equations , 1973 .

[5] Colin W. Cryer. A new class of highly-stable methods:A0-stable methods , 1973 .

[6] W. E. Milne. Numerical Integration of Ordinary Differential Equations , 1926 .

[7] Olof B. Widlund,et al. A note on unconditionally stable linear multistep methods , 1967 .

[8] G. Dahlquist. A special stability problem for linear multistep methods , 1963 .