DIMSEMs - diagonally implicit single-eigenvalue methods for the numerical solution of stiff ODEs on parallel computers. (English) Zbl 0887.65077
The authors present a class of generalized linear methods which are suitable for the solution of stiff ordinary differential equations (ODEs) on parallel computers. The methods are similar to the DIMSIMs of J. C. Butcher [World Sci. Ser. Appl. Anal. 2, 99-111 (1993; Zbl 0834.65059)]. \(A\)-stable DIMSEMs of order 2-6 are derived as well as an \(L\)-stable class of methods which, however, does not possess the single eigenvalue property. A variable stepsize implementation is presented and a comparison with the LSODE code is carried out.
Reviewer: C.Bendtsen (Lyngby)
MSC:
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 34E13 | Multiple scale methods for ordinary differential equations |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65Y05 | Parallel numerical computation |
| 65L50 | Mesh generation, refinement, and adaptive methods for ordinary differential equations |
