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Stability of piecewise polynomial collocation for computing periodic solutions of delay differential equations. (English) Zbl 1002.65089
The authors prove numerical stability for a class of piecewise polynomial collocation methods on nonuniform meshes for computing asymptotically stable and unstable periodic solutions of the linear equation \[ y'(t)= a(t) y(t)+ b(t) y(t-\tau)+ f(t) \] by a (periodic) boundary value approach. Some numerical results are presented.

MSC:
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
34K13 Periodic solutions to functional-differential equations
Software:
COLNEW; COLSYS
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