Numerical methods for solving radial Schro¨dinger equations
Journal of Computational and Applied Mathematics
Automatic solution of Sturm-Liouville problems using the Pruess method
Journal of Computational and Applied Mathematics
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Mathematical software for Sturm-Liouville problems
ACM Transactions on Mathematical Software (TOMS)
Eigenvalue and eigenfunction computations for Sturm-Liouville problems
ACM Transactions on Mathematical Software (TOMS)
CP methods for the Schro¨dinger equation revisited
Journal of Computational and Applied Mathematics
A test package for Sturm-Liouville solvers
ACM Transactions on Mathematical Software (TOMS)
Global Error Estimates for Ordinary Differential Equations
ACM Transactions on Mathematical Software (TOMS)
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)
Symmetric multistep methods over long times
Numerische Mathematik
MATSLISE: A MATLAB package for the numerical solution of Sturm-Liouville and Schrödinger equations
ACM Transactions on Mathematical Software (TOMS)
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An accurate method for the numerical solution of the eigenvalue problem of second-order ordinary differential equation using the shooting method is presented. The method has three steps. Firstly initial values for the eigenvalue and eigenfunction at both ends are obtained by using the discretized matrix eigenvalue method. Secondly the initial-value problem is solved using new, highly accurate formulas of the linear multistep method. Thirdly the eigenvalue is properly corrected at the matching point. The efficiency of the proposed methods is demonstrated by their applications to bound states for the one-dimensional harmonic oscillator, anharmonic oscillators, the Morse potential, and the modified Poschl-Teller potential in quantum mechanics.