A Matrix Method for the Solution of Sturm-Liouville Problems

Pierluigi Amodio , Giuseppina Settanni
Dipartimento di Matematica,
Universita di Bari,
I-70125 Bari, Italy
Received 22 February, 2011; accepted in revised form 13 March, 2011
Abstract: We investigate the numerical solution of regular and singular Sturm-Liouville
problems by means of finite difference schemes of high order. In particular, a set of differ-
ence schemes is used to approximate each derivative independently so to obtain an algebraic
problem corresponding to the original continuous differential equation. The endpoints are
treated depending on their classification and in case of limit points, no boundary condi-
tion is required. Several numerical tests are finally reported on equispaced grids show the
convergence properties of the proposed approach.


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