Closed Newton-Cotes trigonometrically-fitted formulae of high order for the numerical integration of the Schrödinger equation
DOI10.1007/s10910-007-9322-yzbMath1217.65054OpenAlexW2051030570MaRDI QIDQ551947
Publication date: 21 July 2011
Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10910-007-9322-y
numerical methodsSchrödinger equationmultistep methodssymplectic integratorsorbital problemsenergy preservationtrigonometric fittingclosed Newton-Cotes differential methods
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Numerical integration (65D30)
Related Items (50)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A four-step phase-fitted method for the numerical integration of second order initial-value problems
- A Numerov-type method for the numerical solution of the radial Schrödinger equation
- Trigonometrically fitted and exponentially fitted symplectic methods for the numerical integration of the Schrödinger equation
- The numerical solution of the radial Schrödinger equation via a trigonometrically fitted family of seventh algebraic order predictor-corrector methods
- A four-step exponentially fitted method for the numerical solution of the Schrödinger equation
- A family of exponentially-fitted Runge-Kutta methods with exponential order up to three for the numerical solution of the Schrödinger equation
- 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
- A family of embedded Runge-Kutta formulae
- High order embedded Runge-Kutta formulae
- Some embedded modified Runge-Kutta methods for the numerical solution of some specific Schrödinger equations
- A family of hybrid exponentially fitted predictor-corrector methods for the numerical integration of the radial Schrödinger equation
- 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
- Symplectic methods of fifth order for the numerical solution of the radial Schrödinger equation
- A \(P\)-stable exponentially fitted method for the numerical integration of the 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
- Exponentially-fitted multiderivative methods for the numerical solution of the Schrödinger equation
- Embedded methods for the numerical solution of the Schrödinger equation
- A generator of high-order embedded \(P\)-stable 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
- Exponentially fitted symplectic methods for the numerical integration of the Schrödinger equation
- Numerical solution of the two-dimensional time independent Schrödinger equation with Numerov-type methods
- Trigonometrically fitted Runge-Kutta methods for the numerical solution of the Schrödinger equation
- Sixth algebraic order trigonometrically fitted predictor-corrector methods for the numerical solution of the radial Schrödinger equation
- A family of multiderivative methods for the numerical solution of the Schrödinger equation
- Practical points concerning the solution of the Schrödinger equation
- A sixth-order exponentially fitted method for the numerical solution of the radial Schrödinger equation
- Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
- Numerical Methods for y″ =f(x, y) via Rational Approximations for the Cosine
- Symmetric Multistip Methods for Periodic Initial Value Problems
- High Algebraic Order Methods with Minimal Phase-Lag for Accurate Solution of the Schrödinger Equation
- An Eighth Order Exponentially Fitted Method for the Numerical Solution of the Schrödinger Equation
- A NEW NUMEROV-TYPE METHOD FOR COMPUTING EIGENVALUES AND RESONANCES OF THE RADIAL SCHRÖDINGER EQUATION
- 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
This page was built for publication: Closed Newton-Cotes trigonometrically-fitted formulae of high order for the numerical integration of the Schrödinger equation