The Open Numerical Methods Journal

2010, 2 : 1-5
Published online 2010 April 08. DOI: 10.2174/1876389801002010001
Publisher ID: TONUMJ-2-1

S.S. Filippov and A.V. Tygliyan
Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, Miusskaya sq. 4, Moscow 125047, Russia

ABSTRACT

We introduce ABC-schemes, a new class of linearly implicit one-step methods for numerical integration of stiff ordinary differential equation systems. Formulas of ABC-schemes invoke the Jacobian of differential system similary to the methods of Rosenbrock type, but unlike the latter they include also the square of the Jacobian matrix.

Keywords:

Solving stiff ordinary differential equations, Linearly implicit methods, -schemes, -stability, -stability.