Multiderivative methods of eighth algebraic order with minimal phase-lag for the numerical solution of the radial Schrödinger equation
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Publication:1765432
DOI10.1016/j.cam.2004.06.013zbMath1063.65067OpenAlexW2003599516MaRDI QIDQ1765432
D. P. Sakas, Theodore E. Simos
Publication date: 23 February 2005
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2004.06.013
Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05)
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Cites Work
- Unnamed Item
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- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Numerov made explicit has better stability
- A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: Explicit method
- Some embedded modified Runge-Kutta methods for the numerical solution of some specific Schrödinger equations
- Eighth order methods with minimal phase-lag for accurate computations for the elastic scattering phase-shift problem
- A family of trigonometrically-fitted symmetric methods for the efficient solution of the Schrödinger equation and related problems
- Symplectic methods for the numerical solution of the radial Schrödinger equation
- Embedded eighth order methods for the numerical solution of the Schrödinger equation
- Symmetric eighth algebraic order methods with minimal phase-lag for the numerical solution of the Schrödinger equation
- 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
- New P-stable eighth algebraic order exponentially-fitted methods for the numerical integration of the Schrödinger equation
- Family of twelve steps exponential fitting symmetric multistep methods for the numerical solution of the Schrödinger equation
- A family of \(P\)-stable exponentially-fitted methods for the numerical solution of the Schrödinger equation
- Practical points concerning the solution of the Schrödinger equation
- High-Order Embedded Runge-Kutta-Nystrom Formulae
- Numerical Methods for y″ =f(x, y) via Rational Approximations for the Cosine
- Symmetric Multistip Methods for Periodic Initial Value Problems
- On finite difference methods for the solution of the Schrödinger equation
- An Improved Eigenvalue Corrector Formula for Solving the Schrodinger Equation for Central Fields
- A new explicit Bessel and Neumann fitted eighth algebraic order method for the numerical solution of the Schrödinger equation
- A family of P-stable eighth algebraic order methods with exponential fitting facilities
- A generator and an optimized generator of high-order hybrid explicit methods for the numerical solution of the Schrödinger equation. I: Development of the basic method
- A generator and an optimized generator of high-order hybrid explicit methods for the numerical solution of the Schrödinger equation. II: Development of the generator, optimization of the generator and numerical results
- A modified phase-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation
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