Conference publications

Two Stages Singly ROW Methods with Complex Coefficients for Autonomous Systems of ODE

Shirkov P.D., Zubanov A.M.

Компьютерные исследования и моделирование Ижевск: Научно-издательский центр "Регулярная и хаотическая динамика", 2010 (in press). Vol. 2 (1). 21 pp. (accepted)

The basic subset of two-stages Rosenbrock schemes with complex coef-ficients for the numerical solution of autonomous systems of ordinary differential equations (ODE) has been considered. Numerical realization of such schemes demands one LU-decomposition, two computations of right side function and one computation of Jacoby matrix of the system per one step.

The full theoretical investigation of accuracy and stability of such schemes have been done. New A-stable methods of the 3-rd order of accuracy with different properties have been constructed. There are high order L-decremented schemes as well as schemes with simple estimation of the main term of truncation error which is necessary for automatic evolution of time step. Testing of new methods have been done.