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

Alfeld, Peter

doi:10.1090/S0025-5718-1980-0583493-4

A method of skipping the transient phase in the solution of separably stiff ordinary initial value problems
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Math. Comp. 35 (1980), 1173-1176 Request permission

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.

References

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 519719, DOI 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, DOI 10.1090/S0025-5718-1979-0537965-0

BIT

Robert D. Skeel and Antony K. Kong, Blended linear multistep methods, ACM Trans. Math. Software 3 (1977), no. 4, 326–345. MR 461922, DOI 10.1145/355759.355762