Polynomial formulation of second derivative multistep methods

Kovvali, S.; Gupta, G. K.

doi:10.1090/S0025-5718-1982-0645662-6

Polynomial formulation of second derivative multistep methods
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by S. Kovvali and G. K. Gupta PDF

Math. Comp. 38 (1982), 447-458 Request permission

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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