A method of skipping the transient phase in the solution of separably stiff ordinary initial value problems

Author:
Peter Alfeld

Journal:
Math. Comp. **35** (1980), 1173-1176

MSC:
Primary 65L05

DOI:
https://doi.org/10.1090/S0025-5718-1980-0583493-4

MathSciNet review:
583493

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Stiff systems of ordinary differential equations are characterized by an initial phase in which the solution changes rapidly. Often there is no interest in reproducing this transient phase. A method is proposed for modifying the initial value if the system of differential equations is separably stiff, i.e. is characterized by the occurrence of a few (typically one) large negative real eigenvalues which dominate the others. The modified system does not possess a transient phase, and in the constant coefficient linear case its solution does not differ from that of the original one in the nonstiff components.

**[1]**P. ALFELD & J. D. LAMBERT, "Correction in the dominant space: A numerical technique for a certain class of stiff initial value problems,"*Math. Comp.*, v. 31, 1977, pp. 922-938. MR**0519719 (58:24958)****[2]**P. ALFELD, "A special class of explicit linear multistep methods as basic methods for the correction in the dominant space technique,"*Math. Comp.*, v. 33, 1979, pp. 1195-1212. MR**537965 (80h:65045)****[3]**W. H. ENRIGHT, T. E. HULL & B. LINDBERG, "Comparing numerical methods for stiff systems of ODEs,"*BIT*, v. 15, 1975, pp. 10-48.**[4]**R. D. SKEEL & A. K. KONG,*Blended Linear Multistep Methods*, Report UIUCDCS-R-76-800, Department of Computer Science, University of Illinois at Urbana-Champaign, 1976. MR**0461922 (57:1904)**

Retrieve articles in *Mathematics of Computation*
with MSC:
65L05

Retrieve articles in all journals with MSC: 65L05

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1980-0583493-4

Keywords:
Stiff ordinary differential equations,
numerical analysis,
separably stiff systems,
transient phase

Article copyright:
© Copyright 1980
American Mathematical Society