A Newton-Picard collocation method for periodic solutions of delay differential equations

Verheyden, K. & Lust, K., Sep-2005, In : Bit numerical mathematics. 45, 3, p. 605-625 21 p.

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  • Koen Verheyden
  • Kurt Lust

This paper presents a collocation method with an iterative linear system solver to compute periodic solutions of a system of autonomous delay differential equations (DDEs). We exploit the equivalence of the linearized collocation system and the discretization of the linearized periodic boundary value problem (BVP). This linear BVP is solved using a variant of the Newton-Picard method [Int. J. Bifurcation Chaos, 7 (1997), pp. 2547-2560]. This method combines a direct method in the low-dimensional subspace of the weakly stable and unstable modes with an iterative solver in the high-dimensional orthogonal complement. As a side effect, we also obtain good estimates for the dominant Floquet multipliers. We have implemented the method in the DDE-BIFTOOL environment to test our algorithm.

Original languageEnglish
Pages (from-to)605-625
Number of pages21
JournalBit numerical mathematics
Issue number3
Publication statusPublished - Sep-2005


  • delay differential equation, periodic solution, collocation, Newton-Picard, numerical bifurcation analysis, BIFURCATION-ANALYSIS, COMPUTATION, STABILITY

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