NESC9520 KRYSI

1. NAME OR DESIGNATION OF PROGRAM:  KRYSI (ODE solver with SDIRK/Krylov method)

3. DESCRIPTION OF PROGRAM OR FUNCTION

KRYSI is a set of FORTRAN subroutines for solving ordinary differential equations initial value problems. It is suitable for both stiff and nonstiff systems.  When solving the implicit stage equations in the stiff case, KRYSI uses a Krylov subspace iteration method called the SPIGMR (Scaled Preconditioned Incomplete Generalized Minimum Residual) method. No explicit Jacobian storage is required, except where used in pre- conditioning. A demonstration problem is included with a description of two preconditioners that are natural for its solution by KRYSI.

4. METHOD OF SOLUTION

KRYSI uses a three-stage, third-order singly diagonally implicit Runge-Kutta (SDIRK) method. In the stiff case, a preconditioned Krylov subspace iteration within a (so-called) inexact Newton iteration is used to solve the system of nonlinear algebraic equations.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM:

6. TYPICAL RUNNING TIME:  The sample problem required 9 CPU seconds on  a Cray1.

7. UNUSUAL FEATURES OF THE PROGRAM:

8. RELATED AND AUXILIARY PROGRAMS

KRYSI is based on the SIMPLE solver by Norsett and Thomsen. KRYSI solutions compare favorably with LSODPK (NESC 9624), an ODE solver that combines a Backward Differentiation Formula (BDF) method with the SPIGMR algorithm.

10. REFERENCES:

- Alan C. Hindmarsh and Syvert P. Norsett:
  KRYSI, An ODE Solver Combining a Semi-Implicit Runge-Kutta Method
  and a Preconditioned Krylov Method,
  UCID-21422 (May 1988).
- KRYSI, NESC No. 9520, KRYSI Tape Description,
  NESC Note 89-20 (December 6, 1988).

11. MACHINE REQUIREMENTS:  The sample problem required 6960 words on a
Cray1.

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

Both a
single-prevision version for long word-length machines and a double- precision version for short word-length machines are included.

15. NAME AND ESTABLISHMENT OF AUTHORS

  A.C. Hindmarsh
  Computing and Mathematics Research Division
  Lawrence Livermore National Laboratory.
  S.P. Norsett
  Division of Mathematical Sciences
  University of Trondheim
  Norway.

KRYSI Single-Precision FTN77 Source File
LINPACK & BLAS Routines Single-Precision FTN77 source
Demonstration Program Single-Precision FTN77 Source
KRYSI Double-Precision FTN77 Source File
LINPACK & BLAS Routines Double-Precision FTN77 Source
Demonstration Program Double-Precision FTN77 Source
report                   UCID-21422 (May 1988)                      REPPT
prog. note               NESC Note 89-20 (December 6, 1988)         NOTPT