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Abstract
In this paper a study of the existence, uniqueness, stability and convergence of a class of C
2-spline collocation methods for solving delay differential equations (DDEs) is introduced. Letting the interior collocation points , j=1(1)3 be dependent on the parameters c
1, c
2∈(0, 1) and c
3=1 it is shown that the proposed methods for DDEs possess a convergence rate of order six if 58−57(c
1+c
2)+55c
1
c
2=0, and they are unstable if c
1+c
2<1. Moreover, the methods are P-stable for 0.8028≤c
1<c
2. Numerical results illustrating the behaviour of the methods when faced with some difficult problems are presented and the numerical results are compared to those obtained by other methods.
Acknowledgements
The authors are indebted to Professor S. E. El. Gendi for various valuable suggestions and constructive criticism.