Author： AWOYEMI D.O.
Publisher： Taylor & Francis Ltd
ISSN： 0020-7160
Source： International Journal of Computer Mathematics, Vol.80, Iss.8, 2003-08, pp. : 985-991
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Abstract
A P-stable linear multistep method for solving general third order initial value problems of ordinary differential equations without first reducing the problems into a system of first order equations is considered. The approach for the development of this method is essentially based on collocation of the differential system generated from a basis function. A predictor for the evaluation of $y_{n+k}$ for an odd $kge 3$ in the main method is also proposed. The two resulting methods, the corrector and the predictor are P-stable for $k = 3$. These as a block are tested on a number of problems to show their efficiency. When the methods (the corrector and the predictor) are evaluated at $x = x_{n+3}$ identical schemes are obtained as special cases of the methods, while the set of first and second derivatives obtained from the corrector are different from those obtained from the predictor.
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