Thesis (M.Sc.) - Carleton University, 2007. / Includes bibliographical references (p. 81-83). Also available in electronic format on the Internet.

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.