A convergence theorem for Newton-like methods in Banach spaces
Numerische Mathematik
The recovery of potentials from finite spectral data
SIAM Journal on Mathematical Analysis
SIAM Review
Asymptotic correction of Numerov's eigenvalue estimates with natural boundary conditions
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Recovery of the m-function from spectral data for generalized Sturm-Liouville problems
Journal of Computational and Applied Mathematics - Special issue: On the occasion of the eightieth birthday of prof. W.M. Everitt
Exponentially-fitted Numerov methods
Journal of Computational and Applied Mathematics
Numerical solution of the inverse spectral problem for Bessel operators
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
In this paper, we propose a new modified Numerov's method for recovering from eigenvalues a symmetric potential of a Sturm-Liouville operator with Dirichlet boundary conditions. We use interpolation to refine the mesh sufficiently for Numerov's method to be effective even without the asymptotic correction technique of Andrew and Paine. Accuracy and stability of the method are investigated. Convergence of the method is established. Our method is extended to deal with natural boundary conditions. Numerical experiments confirm its competitiveness.