A finite difference method with zero phase-lag and its derivatives for quantum chemistry problems
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Publication:2201026
DOI10.1007/s10910-020-01150-1zbMath1448.81315OpenAlexW3046732271MaRDI QIDQ2201026
Zenggui Wang, Theodore E. Simos
Publication date: 24 September 2020
Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10910-020-01150-1
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) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Computational methods for problems pertaining to quantum theory (81-08) Molecular physics (81V55) Initial value problems for linear higher-order PDEs (35G10)
Related Items
Efficient FinDiff algorithm with optimal phase properties for problems in quantum chemistry, New FD scheme with vanished phase-lag and its derivatives up to order six for problems in chemistry, A new algorithm with eliminated phase-lag and its derivatives up to order five for problems in quantum chemistry, A finite difference method with phase-lag and its derivatives equal to zero for problems in chemistry
Uses Software
Cites Work
- Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)
- Families of Runge-Kutta-Nystrom Formulae
- A P-STABLE EIGHTEENTH-ORDER SIX-STEP METHOD FOR PERIODIC INITIAL VALUE PROBLEMS
- High-accuracy P-stable Methods for y″ = f(t, y)
- Numerical Methods for y″ =f(x, y) via Rational Approximations for the Cosine
- Symmetric Multistip Methods for Periodic Initial Value Problems
- Non-dissipative extended one-step methods for oscillatory problems
- A General Procedure For the Adaptation of Multistep Algorithms to the Integration of Oscillatory Problems
- Exponential-fitted four-step methods for
- Numerical operations on oscillatory functions
- P-stability and exponential-fitting methods for y = f(x,y)
- An improved trigonometrically fitted P-stable Obrechkoff method for periodic initial-value problems
- A PHASE-FITTED AND AMPLIFICATION-FITTED EXPLICIT TWO-STEP HYBRID METHOD FOR SECOND-ORDER PERIODIC INITIAL VALUE PROBLEMS
- Truncation Errors in Exponential Fitting for Oscillatory Problems
- The Numerov method and singular potentials
- Mixed collocation methods for \(y=f(x,y)\)
- A parallel ODE solver adapted to oscillatory problems
- Weights of the exponential fitting multistep algorithms for first-order ODEs
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- 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
- Two new embedded pairs of explicit Runge-Kutta methods adapted to the numerical solution of oscillatory problems
- \(P\)-stable higher derivative methods with minimal phase-lag for solving second order differential equations
- On some new low storage implementations of time advancing Runge-Kutta methods
- 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
- Optimization of explicit two-step hybrid methods for solving orbital and oscillatory problems
- Symmetric and symplectic exponentially fitted Runge-Kutta methods of high order
- A new kind of discretization scheme for solving a two-dimensional time-independent Schrödinger equation
- Arbitrarily precise numerical solutions of the one-dimensional Schrödinger equation
- A hybrid method with phase-lag and derivatives equal to zero for the numerical integration of the Schrödinger equation
- Explicit exponentially fitted two-step hybrid methods of high order for second-order oscillatory IVPs
- Four step methods for \(y=f(x,y)\)
- The arbitrary order implicit multistep schemes of exponential fitting and their applications
- A parallel boundary value technique for singularly perturbed two-point boundary value problems
- Exponentially fitted variable two-step BDF algorithm for first order ODEs
- Comparison of some special optimized fourth-order Runge-Kutta methods for the numerical solution of the Schrödinger equation
- Trigonometrically-fitted method with the Fourier frequency spectrum for undamped Duffing equation
- Obrechkoff one-step method fitted with Fourier spectrum for undamped Duffing equation
- Trigonometrically-fitted method for a periodic initial value problem with two frequencies
- Exponentially fitted symplectic integrators of RKN type for solving oscillatory problems
- Sixth-order symmetric and symplectic exponentially fitted modified Runge-Kutta methods of Gauss type
- Exponential fitting BDF-Runge-Kutta algorithms
- Finite difference approach for the two-dimensional Schrödinger equation with application to scission-neutron emission
- Some procedures for the construction of high-order exponentially fitted Runge-Kutta-Nyström methods of explicit type
- Exponential-fitting methods for the numerical integration of the fourth-order differential equation \(y^{IV}+f\cdot y=g\)
- High-order P-stable multistep methods
- Symplectic conditions for exponential fitting Runge-Kutta-Nyström methods
- On the generation of \(P\)-stable exponentially fitted Runge-Kutta-Nyström methods by exponentially fitted Runge-Kutta methods.
- A new two-step hybrid method for the numerical solution of the Schrödinger equation
- 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
- Structure preservation of exponentially fitted Runge-Kutta methods
- Exponential fitted Gauss, Radau and Lobatto methods of low order
- Sixth-order symmetric and symplectic exponentially fitted Runge-Kutta methods of the Gauss type
- Exponentially-fitted Obrechkoff methods for second-order differential equations
- Accuracy and linear stability of RKN methods for solving second-order stiff problems
- The optimal exponentially-fitted Numerov method for solving two-point boundary value problems
- Unconditionally stable Noumerov-type methods for second order differential equations
- A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems
- Numerov made explicit has better stability
- Phase properties of high order, almost P-stable formulae
- A variable step method for the numerical integration of the one- dimensional Schrödinger equation
- A new class of explicit two-step fourth order methods for \(y=f(t,y)\) with extended intervals of periodicity
- Two-step fourth-order \(P\)-stable methods with phase-lag of order six for \(y=f(t,y)\)
- A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: Explicit method
- Families of two-step fourth order \(P\)-stable methods for second order differential equations
- Numerov method maximally adapted to the Schrödinger equation
- Exponential and Bessel fitting methods for the numerical solution of the Schrödinger equation
- A method for the solution of the Schrödinger equation
- Coleman's method maximally adapted to the Schrödinger equation
- Families of fifth order Nyström methods for y=f(x,y) and intervals of periodicity
- A family of embedded Runge-Kutta formulae
- Intervals of periodicity and absolute stability of explicit Nyström methods for y=f(x,y)
- Two-step methods for the numerical solution of the Schrödinger equation
- Analysis of a family of Chebyshev methods for \(y=f(x,y)\)
- Four-step exponential-fitted methods for nonlinear physical problems
- EXPFIT4 -- a FORTRAN program for the numerical solution of systems of nonlinear second-order initial-value problems
- A conditionally \(P\)-stable fourth-order exponential-fitting method for \(y=f(x,y)\)
- A finite-difference method for the numerical solution of the Schrödinger equation
- A two-stage fourth-order ``almost P-stable method for oscillatory problems
- Dissipative Chebyshev exponential-fitted methods for numerical solution of second-order differential equations.
- Singly-implicit stabilized extended one-step methods for second-order initial-value problems with oscillating solutions
- Trigonometrically fitted nonlinear two-step methods for solving second order oscillatory IVPs
- A generator of families of two-step numerical methods with free parameters and minimal phase-lag
- A finite difference pair with improved phase and stability properties
- New three-stages symmetric two step method with improved properties for second order initial/boundary value problems
- Stability of explicit ARKN methods for perturbed oscillators
- 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
- Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators
- The various order explicit multistep exponential fitting for systems of ordinary differential equations
- Properties and implementation of \(r\)-Adams methods based on mixed-type interpolation
- Exponential Fitting method for the time-dependent Schrödinger equation
- Two-step high order hybrid explicit method for the numerical solution of the Schrödinger equation
- A four-stages multistep fraught in phase method for quantum chemistry problems
- Phase fitted algorithm for problems in quantum chemistry
- An accomplished phase FD process for DEs in chemistry
- A phase fitted FinDiff process for DifEquns in quantum chemistry
- 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
- A perfect in phase FD algorithm for problems in quantum chemistry
- A multiple stage absolute in phase scheme for chemistry problems
- 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
- An economical eighth-order method for the approximation of the solution of the Schrödinger equation
- An explicit Numerov-type method for second-order differential equations with oscillating solutions
- Present state-of-the-art in exponential fitting. A contribution dedicated to Liviu Ixaru on his 70th birthday
- On high order symmetric and symplectic trigonometrically fitted Runge-Kutta methods with an even number of stages
- A trigonometrically fitted explicit hybrid method for the numerical integration of orbital problems
- Adapted BDF algorithms: Higher-order methods and their stability
- New multiple stages two-step complete in phase algorithm with improved characteristics for second order initial/boundary value problems
- New multistage two-step complete in phase scheme with improved properties for quantum chemistry problems
- P-stable high-order super-implicit and Obrechkoff methods for periodic initial value problems
- P-stable exponentially-fitted Obrechkoff methods of arbitrary order for second-order differential equations
- Phase-fitted and amplification-fitted two-step hybrid methods for \(y^{\prime\prime }=f(x,y)\)
- New methods for oscillatory systems based on ARKN methods
- Symplectic explicit methods of Runge-Kutta-Nyström type for solving perturbed oscillators
- The numerical solution of coupled differential equations arising from the Schrödinger equation
- Stabilization of Cowell's method
- Chebyshevian multistep methods for ordinary differential equations
- Frequency evaluation for exponentially fitted Runge-Kutta methods
- \(P\)-stable Obrechkoff methods of arbitrary order for second-order differential equations
