Polynomial formulation of second derivative multistep methods

Authors:
S. Kovvali and G. K. Gupta

Journal:
Math. Comp. **38** (1982), 447-458

MSC:
Primary 65L05

MathSciNet review:
645662

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Abstract: Following the work of Enright [3] there has been interest in studying second derivative methods for solving stiff ordinary differential equations. Successful implementations of second derivative methods have been reported by Enright [3], Sacks-Davis [9], [10] and Addison[l].

Wallace and Gupta [13] have suggested a polynomial formulation of the usual first-derivative multistep methods. Recently Skeel [11] has shown the equivalence of several formulations of multistep methods. The work of Wallace and Gupta [13] was extended to second derivative methods by Gupta [8]. The present work includes results obtained regarding the stability and truncation error of second derivative methods using the polynomial formulation.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1982-0645662-6

Keywords:
Second derivative methods,
multistep methods,
numerical solution of ordinary differential equations,
stiff equations

Article copyright:
© Copyright 1982
American Mathematical Society