Numerical methods and asymptotic error expansions for the Emden-Fowler equations
Authors:
Pedro M. Lima
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Avenida Rovisco Pais, 1096, Lisboa Codex, Portugal
Abstract:
In the present paper we analyse a numerical method for computing the solution of some boundary-value problems for the Emden-Fowler equations. The differential equations are discretized by a finite-difference method and we derive asymptotic expansions for the discretization error. Based on these asymptotic expansions, we use an extrapolation algorithm to accelerate the convergence of the numerical method.