CP methods of higher order for SturmLiouville and Schrdinger equations
The algorithm upon which the code SLCPM12, described in Computer Physics Communications 118 (1999) 259277, is based, is extended to higher order. The implementation of the original algorithm, which was of order {12,10} { 12 , 10 } (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 {14,12} { 14 , 12 } , {16,14} { 16 , 14 } and {18,16} { 18 , 16 } are introduced. Besides regular SturmLiouville and one-dimensional Schrdinger problems also radial Schrdinger equations are considered with potentials of the form V(r)=S(r)/r+R(r) V ( r ) = S ( r ) / r + R ( r ) , where S(r) S ( r ) and R(r) R ( r ) are well behaved functions which tend to some (not necessarily equal) constants when r?0 r ? 0 and r?? r ? ? . Numerical illustrations are given showing the accuracy, the robustness and the CPU-time gain of the proposed algorithms.
schrdinger equation sturmliouville problem eigenvalue problem