SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

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Numerical Solution of Sturm-Liouville Problems via Fer Streamers

A.G.C.P. Ramos and A. Iserles

Abstract
We address the numerical challenge of solving Sturm-Liouville problems in Liouville's normal form with certain boundary conditions. The novelty of our approach, which is based on a non-standard truncation of Fer expansions, which we call Fer streamers, lies in the construction of a numerical method, which does not impose any restriction on the step size, regardless of the size of the eigenvalue. This unique feature paves the way to the initial development of an effective numerical method to compute any eigenvalue, in clear contrast with the state of the art, where it is not feasible to compute large eigenvalues due to restrictions on the step size. Moreover, our theory holds whenever the potential is piecewise analytic and, in each piece, its average is upper bounded by the smallest eigenvalue we seek. We emphasise that our numerical method is at an early stage of development, and comment on our investigation of efficient discretisation schemes for integrals arising in Fer streamers.

Organized by         Universidad de Valladolid     IMUVA