Stabilized cubic c1-spline collocation method for solving first-order ordinary initial value problems

This paper is concerned with a construction of a "variable" one-parameter cubic C 1 -spline collocation method for solving the initial value problem (IVP)viz where the collocation point . The presented method will be shown to be strongly unstable if β ≤ 1/2. It turns out that the proposed...

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Bibliographic Details
Published in:International journal of computer mathematics 2000-01, Vol.74 (1), p.87-96
Main Authors: Sallam, S., Naim Anwar, M.
Format: Article
Language:English
Subjects:
A-stability
A-stabilized Simpson's rule
absolute stability
collocation methods
Exact sciences and technology
First order initial value problem
G.1.7
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Sciences and techniques of general use
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Summary:This paper is concerned with a construction of a "variable" one-parameter cubic C 1 -spline collocation method for solving the initial value problem (IVP)viz where the collocation point . The presented method will be shown to be strongly unstable if β ≤ 1/2. It turns out that the proposed method is a continuous extension of the A-stabilized version of Simpson's rule introduced in [1], if β = 1. Moreover, the method is of order three, for β ∈ (1/2, 1) and is of order four, if β = 1 and y ∈ C 5 [0,b].
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160008804924