Global approximations to solutions of initial value problems

Kramarz, Luis

doi:10.1090/S0025-5718-1978-0461917-1

Global approximations to solutions of initial value problems
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Math. Comp. 32 (1978), 35-59 Request permission

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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