Exponentially fitted TDRK pairs for the Schrödinger equation

DOI10.1007/s10910-015-0500-zzbMath1328.65158OpenAlexW2084494470MaRDI QIDQ500683

Ke Wu, Yanping Yang, Yong Lei Fang

Publication date: 5 October 2015

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

Full work available at URL: https://doi.org/10.1007/s10910-015-0500-z

zbMATH Keywords

error analysisLennard-Jones potentialexponential fittingnumerical resultradial Schrödinger equationtwo-derivative Runge-Kutta methodWoods-Saxon potential

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70)

Cites Work

• Unnamed Item
• Construction of exponentially fitted symplectic Runge-Kutta-Nyström methods from partitioned Runge-Kutta methods
• The use of phase lag and amplification error derivatives for the construction of a modified Runge-Kutta-Nyström method
• A new family of symmetric linear four-step methods for the efficient integration of the Schrödinger equation and related oscillatory problems
• A parametric symmetric linear four-step method for the efficient integration of the Schrödinger equation and related oscillatory problems
• New stable closed Newton-Cotes trigonometrically fitted formulae for long-time integration
• Optimizing a hybrid two-step method for the numerical solution of the Schrödinger equation and related problems with respect to phase-lag
• On the choice of the frequency in trigonometrically-fitted methods for periodic problems
• New modified Runge-Kutta-Nyström methods for the numerical integration of the Schrödinger equation
• 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
• On modified Runge-Kutta trees and methods
• A parallel boundary value technique for singularly perturbed two-point boundary value problems
• Comparison of some special optimized fourth-order Runge-Kutta methods for the numerical solution of the Schrödinger equation
• Exponential fitting BDF-Runge-Kutta algorithms
• Closed Newton-Cotes trigonometrically-fitted formulae of high order for long-time integration of orbital problems
• Trigonometrically fitted fifth-order Runge-Kutta methods for the numerical solution of the Schrödinger equation
• A new two-step hybrid method for the numerical solution of the Schrödinger equation
• On explicit two-derivative Runge-Kutta methods
• On smoothing of the Crank-Nicolson scheme and higher order schemes for pricing barrier options
• 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
• Exponentially and trigonometrically fitted methods for the solution of the Schrödinger equation
• 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
• A family of trigonometrically fitted partitioned Runge-Kutta symplectic 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 family of Runge-Kutta methods with zero phase-lag and derivatives for the numerical solution of the Schrödinger equation and related problems
• A variable step method for the numerical integration of the one- dimensional Schrödinger equation
• An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions
• Newton--Cotes formulae for long-time integration.
• Symplectic integrators for the numerical solution of the Schrödinger equation
• A generator of hybrid symmetric four-step methods for the numerical solution of the Schrödinger equation
• Trigonometrically fitted predictor--corrector methods for IVPs with oscillating solutions
• Dissipative Chebyshev exponential-fitted methods for numerical solution of second-order differential equations.
• Symplectic methods for the numerical solution of the radial Schrödinger equation
• An exponentially-fitted and trigonometrically-fitted method for the numerical solution of periodic initial-value problems.
• An embedded exponentially-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation and related periodic 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
• Dissipative trigonometrically-fitted methods for linear second-order IVPs with oscillating solution.
• An optimized Runge-Kutta method for the solution of orbital problems
• A fourth algebraic order trigonometrically fitted predictor-corrector scheme for IVPs with oscillating solutions
• Multiderivative methods of eighth algebraic order with minimal phase-lag for the numerical solution of the radial Schrödinger equation
• Runge-Kutta methods with minimal dispersion and dissipation for problems arising from computational acoustics
• On the stability of exponential fitting BDF algorithms
• Nonparametric estimation of the logarithmic density derivative of sequences with strong mixing
• 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 new modified embedded 5(4) pair of explicit Runge-Kutta methods for the numerical solution of the Schrödinger equation
• Optimization as a function of the phase-lag order of nonlinear explicit two-step \(P\)-stable method for linear periodic IVPs
• 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
• A family of high-order multistep methods with vanished phase-lag and its derivatives for the numerical solution of the Schrödinger equation
• 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
• Modified explicit Runge-Kutta methods for the numerical solution of the Schrödinger equation
• Exponential fitting BDF algorithms: explicit and implicit 0-stable methods
• Variable stepsize implementation of multistep methods for \(y\prime\prime =f(x,y,y^{\prime})\)
• An efficient numerical method for singular perturbation problems
• Frequency evaluation for exponentially fitted Runge-Kutta methods
• AN EMBEDDED RUNGE–KUTTA METHOD WITH PHASE-LAG OF ORDER INFINITY FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION
• Controlling the error growth in long–term numerical integration of perturbed oscillations in one or several frequencies
• STABILIZATION OF A FOUR-STEP EXPONENTIALLY-FITTED METHOD AND ITS APPLICATION TO THE SCHRÖDINGER EQUATION
• A modified Runge–Kutta method with phase-lag of order infinity for the numerical solution of the Schrödinger equation and related problems
• AN EMBEDDED 5(4) PAIR OF MODIFIED EXPLICIT RUNGE–KUTTA METHODS FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION
• 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
• An exponentially-fitted high order method for long-term integration of periodic initial-value problems