An accomplished phase FD process for DEs in chemistry

DOI10.1007/s10910-019-01067-4zbMath1429.81028OpenAlexW2980497611WikidataQ127096261 ScholiaQ127096261MaRDI QIDQ2278816

Marina A. Medvedeva, Theodore E. Simos

Publication date: 11 December 2019

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

Full work available at URL: https://doi.org/10.1007/s10910-019-01067-4

zbMATH Keywords

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

Mathematics Subject Classification ID

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) Molecular physics (81V55) Initial value problems for PDEs and systems of PDEs with constant coefficients (35E15)

Related Items (27)

A new finite difference method with optimal phase and stability properties for problems in chemistry ⋮ Efficient FinDiff algorithm with optimal phase properties for problems in quantum chemistry ⋮ New FD methods with phase-lag and its derivatives equal to zero for periodic initial value problems ⋮ A new implicit high-order six-step singularly P-stable method for the numerical solution of Schrödinger equation ⋮ A new method with vanished phase-lag and its derivatives of the highest order for problems in quantum chemistry ⋮ A new FinDiff numerical scheme with phase-lag and its derivatives equal to zero for periodic initial value problems ⋮ 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 phase fitted FiniteDiffr process for DiffrntEqutns in chemistry ⋮ A complete in phase FiniteDiffrnc algorithm for DiffrntEqutins in chemistry ⋮ Full in phase finite difference algorithm for differential equations in quantum chemistry ⋮ Phase fitted algorithm for problems in quantum chemistry ⋮ A finite difference method with zero phase-lag and its derivatives for quantum chemistry problems ⋮ Complete in phase method for problems in chemistry ⋮ The new class of multistep multiderivative hybrid methods for the numerical solution of chemical stiff systems of first order IVPs ⋮ A finite difference method with phase-lag and its derivatives equal to zero for problems in chemistry ⋮ Two-step method with vanished phase-lag and its derivatives for problems in quantum chemistry: an economical case ⋮ An economical two-step method with optimal phase and stability properties for problems in chemistry ⋮ A new economical method with eliminated phase-lag and its derivative for problems in chemistry ⋮ A new method with improved phase-lag and stability properties for problems in quantum chemistry - an economical case ⋮ An economical two-step method with improved phase and stability properties for problems in chemistry ⋮ A new improved economical finite difference method for problems in quantum chemistry ⋮ An integrated in phase FD procedure for DiffEqns in chemical problems ⋮ A phase fitted FinDiff process for DifEquns in quantum chemistry ⋮ A complete in phase FinitDiff procedure for DiffEquns in chemistry ⋮ A phase-fitting singularly P-stable economical two-step method for problems in quantum chemistry ⋮ Phase fitted method for quantum chemistry problems

Uses Software

• EXPFIT4
• LaTeX

Cites Work

• 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
• 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 three-stages multistep teeming in phase algorithm for computational problems in chemistry
• A multistage two-step fraught in phase scheme for problems in mathematical chemistry
• 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
• 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 \(y^{\prime\prime }=f(x,y)\)
• A trigonometrically fitted explicit Numerov-type method for second-order initial value problems with oscillating solutions
• 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
• 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

This page was built for publication: An accomplished phase FD process for DEs in chemistry