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We present a convergence analysis of the spectral Lagrange-Galerkin method for mixed periodic/non-periodic convection-diffusion problems. The scheme is unconditionally stable, independent of the diffusion coefficient, even in the case when numerical quadrature is used. The theoretical predictions...
Periodic solutions of certain large-scale systems of ODEs can be computed efficiently using a hybrid Newton-Picard scheme, especially in a continuation context. In this paper we describe and analyse how this approach can be extended to the direct computation of period doubling bifurcation points....