CP methods of higher order for Sturm–Liouville and Schrödinger equations Original Research Article

The algorithm upon which the code SLCPM12, described in Computer Physics Communications 118 (1999) 259–277, is based, is extended to higher order. The implementation of the original algorithm, which was of order image (meaning order 12 at low energies and order 10 at high energies), was more efficient than the well-established codes SL02F, SLEDGE and SLEIGN. In the new algorithm the orders image, image and image are introduced. Besides regular Sturm–Liouville and one-dimensional Schrödinger problems also radial Schrödinger equations are considered with potentials of the form image, where image and image are well behaved functions which tend to some (not necessarily equal) constants when image and image. Numerical illustrations are given showing the accuracy, the robustness and the CPU-time gain of the proposed algorithms.