Abstract

We develop computer-assisted methods of proof for rigorous computation of the Evans function in order to prove stability of traveling waves. We use the parameterization method, series solutions, and the Newton-Kantorovich Theorem to obtain precise, rigorous error bounds for the numerical solution of the ODE used in the construction of the Evans function. We demonstrate these methods on a scalar reaction-diffusion model and on the Gray-Scott model.

Degree

PhD

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

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