Rigorous numerics for ODEs using Chebyshev series and domain decomposition
Rigorous numerics for ODEs using Chebyshev series and domain decomposition
<p style='text-indent:20px;'>In this paper we present a rigorous numerical method for validating analytic solutions of nonlinear ODEs by using Chebyshev-series and domain decomposition. The idea is to define a Newton-like operator, whose fixed points correspond to solutions of the ODE, on the space of geometrically decaying Chebyshev coefficients, and to …