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IMA Journal of Numerical Analysis 1991 11(2):143-158; doi:10.1093/imanum/11.2.143
© 1991 by Institute of Mathematics and its Applications
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Some Applications of the Boundary-Locus Method and the Method of D-Partitions

CHRISTOPHER T. H. BAKER and NEVILLE J. FORD

Department of Mathematics, The Victoria University of Manchester Oxford Road, Manchester M13 9PL
Department of Computer Studies, Chester College of Higher Education Cheyney Road, Chester CH1 4BJ

We summarize aspects of the method of D-partitions and its analogue, the boundary-locus technique. We apply these techniques to a discussion of the stability of the delay equation


Formula

where y(t)={psi}(t), t {varepsilon}[–{tau}, 0]. Some comparisons with results valid for other functional equations are introduced. Of interest are the following features: (i) the results corresponding to our results but applicable to delay-differential equations are not found in the literature, (ii) some unconventional parameter spaces are introduced, and (iii) the possibility of extending results which hold for a basic test equation to more general equations is established.


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