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A \(C^ 1\) interpolant for codes based on backward differentiation formulae. (English) Zbl 0615.65077
The objective of this work is to produce a \(C^ 1\) interpolant for a fixed-step backward differentiation formula with interpolatory step changing, with particular reference to a code which is released in the NAG Library. Although the method essentially consists of augmenting the usual Nordsieck vector, the author shows that it is unnecessary to form this directly, since the correction to the normal vector can be calculated in the interpolation routine. Numerical examples are presented to illustrate the continuity achieved in practice.
Reviewer: J.Oliver

65L05 Numerical methods for initial value problems
34A34 Nonlinear ordinary differential equations and systems, general theory
Full Text: DOI
[1] Berzins, M.; Dew, P.M.; Furzeland, R.M., Software for time-dependent problems, (), a shortened version appeared in · Zbl 0679.65071
[2] Berzins, M.; Furzeland, R.M., A users manual for SPRINT, part 1. algebraic and ordinary differential equations, () · Zbl 0751.65043
[3] Brown, R.L., Recursive calculation of corrector coefficients, ACM SIGNUM newsletter, 8, 12-13, (1973)
[4] Byrne, G.D.; Hindmarsh, A.C., A polyalgorithm for the numerical solution of ordinary differential equations, A.C.M. trans. math. software, 1, 71-96, (1975) · Zbl 0311.65049
[5] Dew, P.M.; West, M., A package for integrating stiff systems of differential equations based on Gear’s method: part 1 department of computer studies, report 111, (1978), The University of Leeds
[6] Enright, W.H.; Hull, T.E.; Lindberg, B., Comparing numerical methods for stiff systems of O.D.E.s, Bit, 15, 10-48, (1975) · Zbl 0301.65040
[7] Gear, C.W., Numerical initial value problems in ordinary differential equations, (1971), Prentice Hall Englewood Cliffs, NJ · Zbl 0217.21701
[8] Hindmarsh, A.C., ODE solvers for use with the method of lines, () · Zbl 0238.65020
[9] Petzold, L., A description of dassl, ()
[10] Shampine, L.F.; Gordon, M.K., Computer solution of O.D.E.s, (1975), Freeman San Francisco, CA · Zbl 0347.65001
[11] Shampine, L.F., Stability properties of Adams methods codes, ACM trans. math. software, 4, 4, (1978) · Zbl 0387.65045
[12] Shampine, L.F., Implementation of implicit O.D.E. formulas for the solution of O.D.E.s, SIAM J. sci. statist. comput., 1, 1, (1980) · Zbl 0463.65050
[13] Shampine, L.F.; Watts, H.A., A smoother interpolant of DE/STEP; INTRP and DEABM, () · Zbl 0591.65052
[14] Watts, H.A., A smoother interpolant of DE/STEP; INSTRP and DEABM, (), (11)
[15] H.A. Watts and L.F. Shampine, Smoother interpolants for Adams Codes, SIAM J. Sci. Statist. Comput., to appear. · Zbl 0591.65052
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