A rigorous implicit C1 Chebyshev integrator for delay equations.

J.P. Lessard and J.D. Mireles James

Abstract: A new approach to validated numerical integration for delay differential equations is given. The method provides mathematically rigorous existence results as well as error bounds for both the solution and the Frechet derivative of the solution with respect to a given past history segment. Chebyshev series are used to discretize the problem, which is approx- imately solved using a standard numerical scheme corrected via Newton's method. The existence/error analysis uses a Newton-Kantorovich argument. We present examples of the rigorous time stepping procedure, and illustrate the use of the method in computer-assisted proofs of existence for periodic solutions of the Mackey-Glass equation.

  • "A rigorous implicit C1 Chebyshev integrator for delay equations"

  • Computer Assisted Proof Codes: (codes require the IntLab and CHEBFUN packages)

  • Compressed Folder Containing all the MatLab/IntLab programs used in the paper.