Convergence acceleration for boundary value problems with singularities using the \(E\)-algorithm (Q1903656)

The paper is concerned with extrapolation methods and asymptotic expansions for finite difference solutions of boundary value problems with linear second-order differential equations. Particular attention is paid to the case where the right-hand side has certain singularities which have to be ``matched'' by the asymptotic expansions. The expansion results are extended to the computation of some integral functional applied to the solution. Finally, some general extrapolation algorithm (``E-algorithm'') exploiting these asymptotic expansions is investigated with respect to its application to the specific situation, and some numerical examples are presented.