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Mathematics of Computation

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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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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