Generalized power asymptotic expansions of solutions to differential equations that depend on parameters are investigated. The changing nature of these expansions as the parameters of the model cross critical values is discussed. An algorithm to identify these critical values and generate the...

In this paper we present MILONGA, a language based on functional programming concepts, which was designed for the implementation of a new generation of nonterm-rewriting elimination algorithms for multivariate polynomial solving [J. Pure Appl. Alg. 124 (1998) 101–146; J. Pure Appl. Alg. 117/118...

In this work, we apply the Lindstedt–Poincaré method in order to seek the periodic solutions of the Barbanis–Contopoulos nonintegrable Hamiltonian system. We first prove that this system admits six nontrivial periodic families in the neighbourhood of the origin. Then we compute the series...

For a simple model problem—the Laplace equation on the unit square with a Dirichlet boundary function vanishing for x = 0, x = 1 and y = 1, and equaling some suitable g(x) for y = 0—we present a proof of convergence for the so-called combination technique, a modern, efficient and easily...