A Neumann series of Bessel functions representation for solutions of Sturm Liouville equations
A Neumann series of Bessel functions (NSBF) representation for solutions of Sturm Liouville equations and for their derivatives is obtained. The representation possesses an attractive feature for applications: for all real values of the spectral parameter \omega $o the estimate of the difference between the exact solution and the approximate one (the truncated NSBF) depends on N (the truncation parameter) and the coefficients of the equation and does not depend on \omega $o. A similar result is valid when \omega \in \mathbb {C}$oC belongs to a strip \left| \hbox {Im \omega \right| <C$$Imo<C. This feature makes the NSBF representation especially useful for applications requiring computation of solutions for large intervals of \omega $o. Error and decay rate estimates are obtained. An algorithm for solving initial value, boundary value or spectral problems for the Sturm Liouville equation is developed and illustrated on a test problem.