Automatic solution of Sturm-Liouville problems using the Pruess method
Journal of Computational and Applied Mathematics
Mathematical software for Sturm-Liouville problems
ACM Transactions on Mathematical Software (TOMS)
CP methods for the Schro¨dinger equation revisited
Journal of Computational and Applied Mathematics
Automatic Solution of the Sturm-Liouville Problem
ACM Transactions on Mathematical Software (TOMS)
CP methods for the Schrödinger equation
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Algorithm 810: The SLEIGN2 Sturm-Liouville Code
ACM Transactions on Mathematical Software (TOMS)
Think globally, act locally: solving highly-oscillatory ordinary differential equations
Applied Numerical Mathematics
MATSLISE: A MATLAB package for the numerical solution of Sturm-Liouville and Schrödinger equations
ACM Transactions on Mathematical Software (TOMS)
RCMS: right correction Magnus series approach for oscillatory ODEs
Journal of Computational and Applied Mathematics
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The main purpose of this paper is to describe the extension of the successful modified integral series methods for Schrödinger problems to more general Sturm-Liouville eigenvalue problems. We present a robust and reliable modified Neumann method which can handle a wide variety of problems. This modified Neumann method is closely related to the second-order Pruess method but provides for higher-order approximations. We show that the method can be successfully implemented in a competitive automatic general-purpose software package.