A method of skipping the transient phase in the solution of separably stiff ordinary initial value problems
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.
-  P. Alfeld and J. D. Lambert, Correction in the dominant space: a numerical technique for a certain class of stiff initial value problems, Math. Comp. 31 (1977), no. 140, 922–938. MR 0519719, https://doi.org/10.1090/S0025-5718-1977-0519719-2
-  Peter Alfeld, A special class of explicit linear multistep methods as basic methods for the correction in the dominant space technique, Math. Comp. 33 (1979), no. 148, 1195–1212. MR 537965, https://doi.org/10.1090/S0025-5718-1979-0537965-0
-  W. H. ENRIGHT, T. E. HULL & B. LINDBERG, "Comparing numerical methods for stiff systems of ODEs," BIT, v. 15, 1975, pp. 10-48.
-  Robert D. Skeel and Antony K. Kong, Blended linear multistep methods, ACM Trans. Math. Software 3 (1977), no. 4, 326–345. MR 0461922, https://doi.org/10.1145/355759.355762
- 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)
- 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)
- W. H. ENRIGHT, T. E. HULL & B. LINDBERG, "Comparing numerical methods for stiff systems of ODEs," BIT, v. 15, 1975, pp. 10-48.
- 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
Keywords: Stiff ordinary differential equations, numerical analysis, separably stiff systems, transient phase
Article copyright: © Copyright 1980 American Mathematical Society