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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

Global approximations to solutions of initial value problems


Author: Luis Kramarz
Journal: Math. Comp. 32 (1978), 35-59
MSC: Primary 65L05
DOI: https://doi.org/10.1090/S0025-5718-1978-0461917-1
MathSciNet review: 0461917
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Abstract: A wide class of implicit one-step methods for the construction of global approximations to solutions of initial value problems is studied. Approximations more general than piecewise polynomials can be constructed to exploit certain characteristics of the differential equation. Error bounds are given for the general class of methods but emphasis is placed on methods based on Hermite interpolation, for which higher rates of convergence are obtained for special choices of interpolation points. Computational examples are presented.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1978-0461917-1
Keywords: Initial value problems, ordinary differential equations, one-step implicit methods, global approximations, collocation, projection methods, piecewise polynomials, spline
Article copyright: © Copyright 1978 American Mathematical Society