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Title: Additive Numerical Methods for Ordinary Differential Equations.
Author: Sayfy, A. M. S.
ISNI:       0000 0001 3554 5471
Awarding Body: University of Sussex
Current Institution: University of Sussex
Date of Award: 1977
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Certain linear methods for numerical integration of x' = f(t,x)"are considered. A method is characterized by a t~iple of matrices (A;B1 ,B2) and a sequence of decompositions of the form f = fl + f 2• When fl = 0 or f2 = 0 an (A;Bl ,B2) method reduces to a linear (A,B) method of the form described by Butcher. Su~ficient conditions for convergence are given. The order of convergence for some types of (A;B l ,B 2 ) methods is established and some methods of both linear multi-step and Runge-Kutta type,are obtained. In particuiar, (A;Bl ,B2) methods up to fourth order are obtained, where the method (A,Bl ) is A-stable and semi-explicit, and where the method (A,B2) is explicit. These methods are suitable for stiff systems of the form x' = A(t)x + g(t,x), since they involve only the solution of linear equations.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available