A new fourteenth algebraic order finite difference method for the approximate solution of the Schrödinger equation

DOI10.1007/s10910-016-0704-xzbMath1422.65329OpenAlexW2556230869MaRDI QIDQ2362129

Jianbin Zhao, Theodore E. Simos

Publication date: 6 July 2017

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

Full work available at URL: https://doi.org/10.1007/s10910-016-0704-x

zbMATH Keywords

initial value problemsSchrödinger equationphase-lagsymmetrichybridmultistepderivative of the phase-lagoscillating solution

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (1)

Algorithm for the development of families of numerical methods based on phase-lag Taylor series

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A new approach on the construction of trigonometrically fitted two step hybrid methods
• A new two stage symmetric two-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the radial Schrödinger equation
• A new four stages symmetric two-step method with vanished phase-lag and its first derivative for the numerical integration of the Schrödinger equation
• Construction of exponentially fitted symplectic Runge-Kutta-Nyström methods from partitioned Runge-Kutta methods
• An optimized two-step hybrid block method for solving general second order initial-value problems
• A new high algebraic order four stages symmetric two-step method with vanished phase-lag and its first and second derivatives for the numerical solution of the Schrödinger equation and related problems
• A new optimized symmetric 8-step semi-embedded predictor-corrector method for the numerical solution of the radial Schrödinger equation and related orbital problems
• 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
• An explicit four-step method with vanished phase-lag and its first and second derivatives
• A Runge-Kutta type four-step method with vanished phase-lag and its first and second derivatives for each level for the numerical integration of the Schrödinger equation
• A family of explicit linear six-step methods with vanished phase-lag and its first derivative
• A hybrid type four-step method with vanished phase-lag and its first, second and third derivatives for each level for the numerical integration of the Schrödinger equation
• An eight-step semi-embedded predictor-corrector method for orbital problems and related IVPs with oscillatory solutions for which the frequency is unknown
• A high algebraic order predictor-corrector explicit method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the Schrödinger equation and related problems
• Efficient low computational cost hybrid explicit four-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical integration of the Schrödinger equation
• A high algebraic order multistage explicit four-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives for the numerical solution of the Schrödinger equation
• An efficient numerical method for the solution of the Schrödinger equation
• New modified Runge-Kutta-Nyström methods for the numerical integration of the Schrödinger equation
• 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 dissipative exponentially-fitted method for the numerical solution of the Schrödinger equation and related problems
• High order closed Newton-Cotes exponentially and trigonometrically fitted formulae as multilayer symplectic integrators and their application to the radial Schrödinger equation
• Closed Newton-Cotes trigonometrically-fitted formulae of high order for long-time integration of orbital problems
• A four-step phase-fitted method for the numerical integration of second order initial-value problems
• High-order P-stable multistep methods
• Two optimized symmetric eight-step implicit methods for initial-value problems with oscillating solutions
• A new family of two stage symmetric two-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation
• Exponentially and trigonometrically fitted methods for the solution of the Schrödinger equation
• 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
• A new Numerov-type method for the numerical solution of the Schrödinger equation
• Phase properties of high order, almost P-stable formulae
• A variable step method for the numerical integration of the one- dimensional Schrödinger equation
• 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
• A finite-difference method for the numerical solution of the Schrödinger equation
• 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
• Zero dissipative, explicit Numerov-type methods for second order IVPs with oscillating solutions
• An exponentially-fitted and trigonometrically-fitted method for the numerical solution of periodic initial-value problems.
• 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
• An explicit sixth-order method with phase-lag of order eight for \(y=f(t,y)\)
• Comparison of some four-step methods for the numerical solution of the Schrödinger equation
• New high order multiderivative explicit four-step methods with vanished phase-lag and its derivatives for the approximate solution of the Schrödinger equation. I: construction and theoretical analysis
• Two-step high order hybrid explicit method 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
• A Runge-Kutta type implicit high algebraic order two-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of coupled differential equations arising from the Schrödinger equation
• A predictor-corrector explicit four-step method with vanished phase-lag and its first, second and third derivatives for the numerical integration of the Schrödinger equation
• A family of high-order multistep methods with vanished phase-lag and its derivatives for the numerical solution of the Schrödinger equation
• The numerical solution of coupled differential equations arising from the Schrödinger equation
• Stabilization of Cowell's method
• Chebyshevian multistep methods for ordinary differential equations
• Families of Runge-Kutta-Nystrom Formulae
• Symmetric Multistip Methods for Periodic Initial Value Problems
• A new high algebraic order efficient finite difference method for the solution of the Schrödinger equation

This page was built for publication: A new fourteenth algebraic order finite difference method for the approximate solution of the Schrödinger equation