Polynomial formulation of second derivative multistep methods
Authors:
S. Kovvali and G. K. Gupta
Journal:
Math. Comp. 38 (1982), 447458
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], SacksDavis [9], [10] and Addison[l]. Wallace and Gupta [13] have suggested a polynomial formulation of the usual firstderivative 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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 G. K. Gupta, "Implementing second derivative multistep methods using the Nordsieck polynomial representation," Math. Comp., v. 32, 1978, pp. 1318. MR 0478630 (57:18107)
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 R. D. Skeel, "Equivalent forms of multistep formulas," Math. Comp., v. 33, 1979, pp. 12291250. MR 537967 (80j:65027)
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 R. D. Skeel & A. K. Kong, "Blended linear multistep methods," ACM Trans. Math. Software, v. 3, 1977, pp. 326345 (also Report UIUCDCSR76800, Dept. of Computer Science, Univ. of Illinois). MR 0461922 (57:1904)
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 C. S. Wallace & G. K. Gupta, "General linear multistep methods to solve ordinary differential equations," Austral. Comput. J., v. 5, 1973, pp. 6269. MR 0362919 (50:15357)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198206456626
PII:
S 00255718(1982)06456626
Keywords:
Second derivative methods,
multistep methods,
numerical solution of ordinary differential equations,
stiff equations
Article copyright:
© Copyright 1982
American Mathematical Society
