New hybrid two-step method with optimized phase and stability characteristics
From MaRDI portal
Publication:1617569
DOI10.1007/s10910-018-0894-5zbMath1402.81137OpenAlexW2791096768WikidataQ130122152 ScholiaQ130122152MaRDI QIDQ1617569
A. A. Bondarenko, Ruslan V. Fedorov, Vladislav N. Kovalnogov, Theodore E. Simos
Publication date: 8 November 2018
Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10910-018-0894-5
initial value problemsSchrödinger equationphase-lagsymmetrichybridmultistepderivative of the phase-lagoscillating solution
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Computational methods for problems pertaining to quantum theory (81-08)
Related Items (17)
New Runge-Kutta type symmetric two-step method with optimized characteristics ⋮ A new family of explicit linear two-step singularly P-stable Obrechkoff methods for the numerical solution of second-order IVPs ⋮ New multiple stages two-step complete in phase algorithm with improved characteristics for second order initial/boundary value problems ⋮ New four stages multistep in phase algorithm with best possible properties for second order problems ⋮ New multistage two-step complete in phase scheme with improved properties for quantum chemistry problems ⋮ A new multistage multistep full in phase algorithm with optimized characteristics for problems in chemistry ⋮ A new four-stages two-step phase fitted scheme for problems in quantum chemistry ⋮ New Runge-Kutta type symmetric two step finite difference pair with improved properties for second order initial and/or boundary value problems ⋮ A new multistep method with optimized characteristics for initial and/or boundary value problems ⋮ New multiple stages scheme with improved properties for second order problems ⋮ New three-stages symmetric two step method with improved properties for second order initial/boundary value problems ⋮ New hybrid symmetric two step scheme with optimized characteristics for second order problems ⋮ A three-stages multistep teeming in phase algorithm for computational problems in chemistry ⋮ A four-stages multistep fraught in phase method for quantum chemistry problems ⋮ Algorithm for the development of families of numerical methods based on phase-lag Taylor series ⋮ A multistage two-step fraught in phase scheme for problems in mathematical chemistry ⋮ A Runge-Kutta type crowded in phase algorithm for quantum chemistry problems
Uses Software
Cites Work
- Unnamed Item
- 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 high-order two-step phase-fitted method for the numerical solution of the Schrödinger equation
- 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 new explicit hybrid four-step method with vanished phase-lag and its derivatives
- 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
- A low computational cost eight algebraic order hybrid method with vanished phase-lag and its first, second, third and fourth derivatives for the approximate 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.
- New five-stages two-step method with improved characteristics
- A four stages numerical pair with optimal phase and stability properties
- A finite difference pair with improved phase and stability properties
- A hybrid finite difference pair with maximum phase and stability properties
- New finite difference pair with optimized phase and stability properties
- 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
- Phase-fitted Runge-Kutta pairs of orders 8(7)
- An economical eighth-order method for the approximation of the solution of the Schrödinger equation
- An efficient and computational effective method for second order problems
- 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
- New five-stages finite difference pair with optimized phase properties
- A five-stages symmetric method with improved phase properties
- Families of Runge-Kutta-Nystrom Formulae
- Evolutionary generation of high-order, explicit, two-step methods for second-order linear IVPs
- A new family of 7 stages, eighth-order explicit Numerov-type methods
- Symmetric Multistip Methods for Periodic Initial Value Problems
- Modified two‐step hybrid methods for the numerical integration of oscillatory problems
- Trigonometric fitted, eighth‐order explicit Numerov‐type methods
- A new high algebraic order efficient finite difference method for the solution of the Schrödinger equation
- Conditions for Trigonometrically Fitted Runge-Kutta Methods
- Analytical Mechanics for Relativity and Quantum Mechanics
This page was built for publication: New hybrid two-step method with optimized phase and stability characteristics
