Trigonometrically fitted high-order predictor-corrector method with phase-lag of order infinity for the numerical solution of radial Schrödinger equation
DOI10.1007/s10910-014-0353-xzbMath1301.65075OpenAlexW1979897682MaRDI QIDQ460949
Publication date: 9 October 2014
Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10910-014-0353-x
numerical examplesinitial value problemsSchrödinger equationphase-lagsymmetric multistep methodsoscillating solutionpredictor-correctorresonance problemorbital problems
Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Linear ordinary differential equations and systems (34A30) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)
Related Items (8)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Construction of exponentially fitted symplectic Runge-Kutta-Nyström methods from partitioned Runge-Kutta methods
- A new phase-fitted eight-step symmetric embedded predictor-corrector method (EPCM) for orbital problems and related IVPs with oscillating solutions
- New open modified Newton Cotes type formulae as multilayer symplectic integrators
- A new optimized symmetric 8-step semi-embedded predictor-corrector method for the numerical solution of the radial Schrödinger equation and related orbital 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
- The new class of implicit \(L\)-stable hybrid Obrechkoff method for the numerical solution of first order initial value problems
- Symplectic partitioned Runge-Kutta methods with minimal phase-lag
- A nonlinear explicit two-step fourth algebraic order method of order infinity for linear periodic initial value problems
- P-stability, trigonometric-fitting and the numerical solution of the radial Schrödinger equation
- 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
- A new two-step P-stable hybrid Obrechkoff method for the numerical integration of second-order IVPs
- 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
- Symmetric multistep Obrechkoff methods with zero phase-lag for periodic initial value problems of second order differential equations
- A two-step method with vanished phase-lag and its first two derivatives for the numerical solution of the Schrödinger equation
- On modified Runge-Kutta trees and methods
- A dissipative exponentially-fitted method for the numerical solution of the Schrödinger equation and related problems
- A new high efficient and high accurate Obrechkoff four-step method for the periodic nonlinear undamped Duffing's equation
- A new kind of high-efficient and high-accurate P-stable Obrechkoff three-step method for periodic initial-value problems
- A phase-fitted Runge-Kutta-Nyström method for the numerical solution of initial value problems with oscillating solutions
- 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
- High-order P-stable multistep methods
- \(P\)-stable symmetric super-implicit methods for periodic initial value problems
- Symplectic conditions for exponential fitting Runge-Kutta-Nyström methods
- A family of two-stage two-step methods for the numerical integration of the Schrödinger equation and related IVPs with oscillating solution
- Two optimized symmetric eight-step implicit methods for initial-value problems with oscillating solutions
- An optimized explicit Runge-Kutta method with increased phase-lag order for the numerical solution of the Schrödinger equation and related problems
- A family of exponentially-fitted Runge-Kutta methods with exponential order up to three for the numerical solution of the Schrödinger equation
- Exponentially and trigonometrically fitted methods for the solution of the Schrödinger equation
- On the frequency choice in trigonometrically fitted methods
- A new Numerov-type method for the numerical solution of the Schrödinger equation
- A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: Explicit method
- Explicit high order methods for the numerical integration of periodic initial-value problems
- Symmetric eighth algebraic order methods with minimal phase-lag for the numerical solution of the Schrödinger equation
- Multiderivative methods of eighth algebraic order with minimal phase-lag for the numerical solution of the radial Schrödinger equation
- Exponentially-fitted multiderivative methods for the numerical solution of the Schrödinger equation
- An explicit hybrid method of Numerov type for second-order periodic initial-value problems
- High order four-step hybrid method with vanished phase-lag and its derivatives for the approximate 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
- A symmetric eight-step predictor-corrector method for the numerical solution of the radial Schrödinger equation and related IVPs with oscillating solutions
- An optimized explicit Runge-Kutta-Nyström method for the numerical solution of orbital and related periodical initial value problems
- Optimization as a function of the phase-lag order of nonlinear explicit two-step \(P\)-stable method for linear periodic IVPs
- A family of high-order multistep methods with vanished phase-lag and its derivatives for the numerical solution of the Schrödinger equation
- P-stable exponentially-fitted Obrechkoff methods of arbitrary order for second-order differential equations
- 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
- A family of multiderivative methods for the numerical solution of the Schrödinger equation
- Variable stepsize implementation of multistep methods for \(y\prime\prime =f(x,y,y^{\prime})\)
- Numerical integration of ordinary differential equations based on trigonometric polynomials
- Stabilization of Cowell's method
- A NEW SYMMETRIC EIGHT-STEP PREDICTOR-CORRECTOR METHOD FOR THE NUMERICAL SOLUTION OF THE RADIAL SCHRÖDINGER EQUATION AND RELATED ORBITAL PROBLEMS
- P-Stable Obrechkoff Methods with Minimal Phase-Lag for Periodic Initial Value Problems
- Symmetric Multistip Methods for Periodic Initial Value Problems
- On accuracy and unconditional stability of linear multistep methods for second order differential equations
- A P-stable complete in phase Obrechkoff trigonometric fitted method for periodic initial-value problems
- Effective Numerical Approximation of Schrödinger type Equations through Multiderivative Exponentially-fitted Schemes
- A NEW METHODOLOGY FOR THE CONSTRUCTION OF OPTIMIZED RUNGE–KUTTA–NYSTRÖM METHODS
- TWO NEW PHASE-FITTED SYMPLECTIC PARTITIONED RUNGE–KUTTA METHODS
- An improved trigonometrically fitted P-stable Obrechkoff method for periodic initial-value problems
- An exponentially-fitted high order method for long-term integration of periodic initial-value problems
This page was built for publication: Trigonometrically fitted high-order predictor-corrector method with phase-lag of order infinity for the numerical solution of radial Schrödinger equation