Stability of Numerical Methods for Retarded Functional Differential

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Date
2015-06-22
Authors
El Nubi, Ahmed Osman
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UOFK
Abstract
This study deals with two problems 10 the stability of numerical methods for retarded functional differential equatiol1s. The first problem is that of absolute stability and the second is A-stability. The investigation of the two problerns in the field of ordinary differential equations has been going on for the last two deadest. In the first chapter we review the existence and uniqueness of-the solution and the question of interpolation of the retarded functional equation. We then proceed to throw some light on the main results of the two types of stabilities in the field of initial valley problems of ordinary and delay differential equations whose delay is a constant. Chapter 2 and 3 are devoted to the theory of F-stability and its development. Numerical results are supplemental in Chapter 3. In the last chapter we deal with the problem of A-stability and to how far the known results for initial value problems of ordinary and delay differential equations can be extended to retarded functional differential equations.
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Keywords
numerical methods, the theory of F-stability
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