An improved version of the reduction to scalar CDS method for the numerical solution of separably stiff initial value problems

Author:
Peter Alfeld

Journal:
Math. Comp. **33** (1979), 535-539

MSC:
Primary 65L05

DOI:
https://doi.org/10.1090/S0025-5718-1979-0521274-X

MathSciNet review:
521274

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Abstract: In [1] the Reduction to Scalar CDS method for the solution of separably stiff initial value problems is proposed. In this paper an improved version is given that is equivalent for linear problems but considerably superior for nonlinear problems. A naturally arising numerical example is given, for which the old version fails, yet the new version yields very good results. The disadvantage of the new version is that in the case of several dominant eigenvalues , say, a system of *s* nonlinear equations has to be solved, whereas the old version gives rise to *s* uncoupled nonlinear equations.

**[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, "Inverse linear multistep methods for the numerical solution of initial value problems of ordinary differential equations,"*Math. Comp.*, v. 33, 1979, pp. 111-124. MR**514813 (80b:65092)****[3]**W. E. ENRIGHT, T. E. HULL & B. LINDBERG, "Comparing numerical methods for stiff systems of o.d.e.s,"*BIT*, v. 15, 1975, pp. 10-48.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1979-0521274-X

Keywords:
Ordinary differential equations,
numerical solution,
stiff initial value problems,
correction in the cominant space

Article copyright:
© Copyright 1979
American Mathematical Society