A new family of exponentially fitted methods

DOI10.1016/S0895-7177(03)90028-8zbMath1051.65080OpenAlexW2037428996MaRDI QIDQ597524

P. S. Williams, Theodore E. Simos

Publication date: 6 August 2004

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0895-7177(03)90028-8

zbMATH Keywords

differential equationsSchrödinger equationFinite-difference methodsBound-states problemCoupledDissipative methodsExponentially-fittedMultistep methodsResonance problemScattering problemsVariable-step method

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

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Cites Work

• Unnamed Item
• Unnamed Item
• Numerical methods for solving radial Schrödinger equations
• A four-step method for the numerical solution of the Schrödinger equation
• A variable step method for the numerical integration of the one- dimensional Schrödinger equation
• Runge-Kutta-Nyström triples
• A new variable step method for the numerical integration of the one- dimensional Schrödinger equation
• Exponential and Bessel fitting methods for the numerical solution of the Schrödinger equation
• Two-step methods for the numerical solution of the Schrödinger equation
• Some embedded modified Runge-Kutta methods for the numerical solution of some specific Schrödinger equations
• A family of hybrid exponentially fitted predictor-corrector methods for the numerical integration of the radial Schrödinger equation
• A family of Numerov-type exponentially fitted predictor-corrector methods for the numerical integration of the radial Schrödinger equation
• Practical points concerning the solution of the Schrödinger equation
• The numerical solution of coupled differential equations arising from the Schrödinger equation
• Chebyshevian multistep methods for ordinary differential equations
• A sixth-order exponentially fitted method for the numerical solution of the radial Schrödinger equation
• Solving Ordinary Differential Equations I
• Some New Four-Step Exponential-Fitting Methods for the Numerical Solution of the Radical Schrödinger Equation
• High-Order Embedded Runge-Kutta-Nystrom Formulae
• Shooting methods for the Schrodinger equation
• Numerical Methods for y″ =f(x, y) via Rational Approximations for the Cosine
• On computing eigenvalues of the Schrodinger equation for symmetrical potentials
• Symmetric Multistip Methods for Periodic Initial Value Problems
• Dissipative exponentially-fitted methods for the numerical solution of the Schrödinger equation
• An Improved Eigenvalue Corrector Formula for Solving the Schrodinger Equation for Central Fields