A-stable, accurate averaging of multistep methods for stiff differential equations

Authors:
W. Liniger;F. Odeh
Affiliations:
IBM Thomas J. Watson Research Center, Yorktown Heights, New York;IBM Thomas J. Watson Research Center, Yorktown Heights, New York
Venue:
IBM Journal of Research and Development
Year:
1972

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Abstract

Several low-order numerical solutions of stiff systems of ordinary differential equations are computed by repeated integration, using a multistep formula with parameters. By forming suitable linear combinations of such solutions, higher-order solutions are obtained. If the parameters are properly chosen the underlying solutions, and thus the higher-order one, can be madAe A-stable and strongly damping with respect to the stiff components of the system. A detailed description is given of an algorithmic implementation of the method, which is computationally efficient. Numerical experiments are carried out on some test problems, confirming the validity of the method.