New optimized explicit modified RKN methods for the numerical solution of the Schrödinger equation

DOI10.1007/s10910-012-0090-yzbMath1447.81109OpenAlexW2079330705MaRDI QIDQ1936977

Xiong You, Qinghe Ming, Yong Lei Fang

Publication date: 11 February 2013

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-012-0090-y

zbMATH Keywords

dissipationdispersionSchrödinger equationmodified Runge-Kutta-Nyström methods

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations (37L05)

Related Items (4)

A new phase-fitted eight-step symmetric embedded predictor-corrector method (EPCM) for orbital problems and related IVPs with oscillating solutions ⋮ A 6(4) optimized embedded Runge-Kutta-Nyström pair for the numerical solution of periodic problems ⋮ New 8-step symmetric embedded predictor-corrector (EPCM) method with vanished phase-lag and its first derivative for the numerical integration of the Schrödinger equation ⋮ New optimized symmetric and symplectic trigonometrically fitted RKN methods for second-order oscillatory differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Optimizing a hybrid two-step method for the numerical solution of the Schrödinger equation and related problems with respect to phase-lag
• A new hybrid two-step method with vanished phase-lag and its first and second derivatives for the numerical solution of the Schrödinger equation and related problems
• ERKN integrators for systems of oscillatory second-order differential equations
• A family of eight-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation
• Closed Newton-Cotes trigonometrically-fitted formulae of high order for the numerical integration of the Schrödinger equation
• P-stability, trigonometric-fitting and the numerical solution of the radial Schrödinger equation
• Computation of the eigenvalues of the Schrödinger equation by exponentially-fitted Runge-Kutta-Nyström methods
• High algebraic order methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation
• Mulitstep methods with vanished phase-lag and its first and second derivatives for the numerical integration of the Schrödinger equation
• Special issue: Advances in computational and mathematical methods in science and engineering (CMMSE 2009). Selected papers based on the presentations at the conference, Gijón, Spain, June 26--July 1, 2009.
• A numerical ODE solver that preserves the fixed points and their stability
• Construction of an optimized explicit Runge-Kutta-Nyström method for the numerical solution of oscillatory initial value problems
• A parallel boundary value technique for singularly perturbed two-point boundary value problems
• A dissipative exponentially-fitted method for the numerical solution of the Schrödinger equation and related problems
• Exponential fitting BDF-Runge-Kutta algorithms
• Closed Newton-Cotes trigonometrically-fitted formulae of high order for long-time integration of orbital problems
• A new two-step hybrid method for the numerical solution of the Schrödinger equation
• Trigonometrically fitted and exponentially fitted symplectic methods for the numerical integration of the Schrödinger equation
• Exponential fitted Gauss, Radau and Lobatto methods of low order
• An embedded phase-fitted modified Runge-Kutta method for the numerical integration of the radial Schrödinger equation
• On the frequency choice in trigonometrically fitted methods
• High order closed Newton-Cotes trigonometrically-fitted formulae for the numerical solution of the Schrödinger equation
• Multistep numerical methods for the integration of oscillatory problems in several frequencies
• A \(5(3)\) pair of explicit Runge-Kutta-Nyström methods for oscillatory problems
• A new Numerov-type method for the numerical solution of the Schrödinger equation
• 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
• Newton--Cotes formulae for long-time integration.
• Symplectic integrators for the numerical solution of the Schrödinger equation
• Dissipative Chebyshev exponential-fitted methods for numerical solution of second-order differential equations.
• 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
• Embedded eighth order methods for the numerical solution of the Schrödinger equation
• An embedded exponentially-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation and related periodic initial-value problems
• 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
• On the stability of exponential fitting BDF algorithms
• Comparison of some four-step methods for the numerical solution of the Schrödinger equation
• 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
• Trigonometrically-fitted Scheifele two-step methods for perturbed oscillators
• Symmetric and symplectic ERKN methods for oscillatory Hamiltonian systems
• An optimized explicit Runge-Kutta-Nyström method for the numerical solution of orbital and related periodical initial value problems
• Exponentially-fitted explicit Runge-Kutta methods
• A family of \(P\)-stable exponentially-fitted methods for the numerical solution of the Schrödinger equation
• Numeric multistep variable methods for perturbed linear system integration
• Exponential fitting BDF algorithms and their properties
• Adapted BDF algorithms: Higher-order methods and their stability
• New second-order exponentially and trigonometrically fitted symplectic integrators for the numerical solution of the time-independent 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
• Exponential fitting BDF algorithms: explicit and implicit 0-stable methods
• Frequency evaluation for exponentially fitted Runge-Kutta methods
• A NEW MODIFIED RUNGE–KUTTA–NYSTRÖM METHOD WITH PHASE-LAG OF ORDER INFINITY FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION AND RELATED PROBLEMS
• Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
• Controlling the error growth in long–term numerical integration of perturbed oscillations in one or several frequencies
• Solving Ordinary Differential Equations I
• STABILIZATION OF A FOUR-STEP EXPONENTIALLY-FITTED METHOD AND ITS APPLICATION TO THE SCHRÖDINGER EQUATION
• Symmetric Multistip Methods for Periodic Initial Value Problems
• P-stability and exponential-fitting methods for y = f(x,y)
• Mixed collocation methods for \(y=f(x,y)\)
• 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: New optimized explicit modified RKN methods for the numerical solution of the Schrödinger equation