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Frequency analysis of preconditioned waveform relaxation iterations

100%

Augustynowicz A., Jackiewicz Z.

Applicationes Mathematicae

1999

tom 26

nr 2

229-242

The error analysis of preconditioned waveform relaxation iterations for differential systems is presented. This analysis extends and refines previous results by Burrage, Jackiewicz, Nørsett and Renaut by incorporating all terms in the expansion of the error of waveform relaxation iterations in the Laplace transform domain. Lower bounds for the size of the window of rapid convergence are also obtained. The theory is illustrated for waveform relaxation methods applied to differential systems resulting from semi-discretization of the heat equation in one and two dimensions. This theory and some heuristic arguments predict that preconditioning is most effective for the first few iterations.

Toward a two-step Runge-Kutta code for nonstiff differential systems

100%

Bartoszewski Z., Jackiewicz Z.

Applicationes Mathematicae

2001

tom 28

nr 3

353-365

Various issues related to the development of a new code for nonstiff differential equations are discussed. This code is based on two-step Runge-Kutta methods of order five and stage order five. Numerical experiments are presented which demonstrate that the new code is competitive with the Matlab ode45 program for all tolerances.

Ograniczanie wyników

2 Applicationes Mathematicae

2 Jackiewicz Z.

1 Augustynowicz A.

1 Bartoszewski Z.

1 2001

1 1999

Wyniki wyszukiwania

Frequency analysis of preconditioned waveform relaxation iterations

Toward a two-step Runge-Kutta code for nonstiff differential systems