Matrix-free methods in the solution of stiff systems of ODE's
Technical Report
·
OSTI ID:5507301
This is an informal preliminary report, on a study of a matrix-free method for solving stiff systems of ordinary differential equations (ODE's). In the numerical time integration of stiff ODE initial value problems by BDF methods, the resulting nonlinear algebraic system is usually solved by a modified Newton method and an appropriate linear sytem algorithm. In place of that, we substitute Newton's method (unmodified) coupled with an iterative linear system method. The latter is a projection method called the Incomplete Orthogonalization Method (IOM), developed mainly by Y. Saad. A form of IOM, with scaling included to enhance robustness, is studied in the setting of Inexact Newton Methods, and implemented in a way that requires no matrix storage whatever. Tests on several stiff problems, of sizes up to 5000, show the method to be quite effective, and much more economical, in both computational cost and storage, than standard solution methods.
- Research Organization:
- Lawrence Livermore National Lab., CA (USA)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 5507301
- Report Number(s):
- UCID-19937; ON: DE84003361
- Country of Publication:
- United States
- Language:
- English
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