Stability of piecewise polynomial collocation for computing periodic solutions of delay differential equations. (English) Zbl 1002.65089

Engelborghs, K.; Doedel, E. J.

Numer. Math. 91, No. 4, 627-648 (2002).

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.

Reviewer: Laura-Iulia Aniţa (Iaşi)

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

Keywords:

piecewise polynomial collocation methods; periodic solutions; delay differential equations; stability; nonuniform meshes; numerical results

Software:

COLNEW; COLSYS