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

MathSciNet review:
583493

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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 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**, 10.1090/S0025-5718-1977-0519719-2**[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**, 10.1090/S0025-5718-1979-0537965-0**[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]**Robert D. Skeel and Antony K. Kong,*Blended linear multistep methods*, ACM Trans. Math. Software**3**(1977), no. 4, 326–345. MR**0461922**

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DOI:
http://dx.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