A variable-step Numerov method for the numerical solution of the Schrödinger equation
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Publication:2485886
DOI10.1007/s10910-004-1467-3zbMath1070.81513OpenAlexW2035377053MaRDI QIDQ2485886
Higinio Ramos, Jesus Vigo Aguiar
Publication date: 5 August 2005
Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10910-004-1467-3
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Computational methods for problems pertaining to quantum theory (81-08) Molecular physics (81V55)
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Cites Work
- Unnamed Item
- Experiments in stepsize control for Adams linear multistep methods
- Two-step methods for the numerical solution of the Schrödinger equation
- Analysis of a family of Chebyshev methods for \(y=f(x,y)\)
- Unconditionally stable methods for second order differential equations
- A P-stable singly diagonally implicit Runge-Kutta-Nyström method
- Some embedded modified Runge-Kutta methods for the numerical solution of some specific Schrödinger equations
- A new numerical method for the integration of highly oscillatory second-order ordinary differential equations
- Variable-order, variable-step methods for second-order initial-value problems
- Construction of trigonometrically and exponentially fitted Runge--Kutta--Nyström methods for the numerical solution of the Schrödinger equation and related problems -- a method of 8th algebraic order
- Practical points concerning the solution of the Schrödinger equation
- New insights in the development of Numerov-type methods with minimal phase-lag for the numerical solution of the Schrödinger equation
- High order Bessel fitting methods for the numerical integration of the Schrödinger equation
- Effective Numerical Approximation of Schrödinger type Equations through Multiderivative Exponentially-fitted Schemes
- On finite difference methods for the solution of the Schrödinger equation
- A family of P-stable eighth algebraic order methods with exponential fitting facilities
- A note on the step size selection in Adams multistep methods
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