A family of four-step exponentially fitted predictor-corrector methods for the numerical integration of the Schrödinger equation

DOI10.1016/0377-0427(93)E0274-PzbMath0833.65082MaRDI QIDQ1899961

Theodore E. Simos

Publication date: 14 March 1996

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Schrödinger differential equationfour-step exponentially fitted predictor-corrector methods

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (15)

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 ⋮ A new methodology for the development of numerical methods for the numerical solution of the Schrödinger equation ⋮ A new methodology for the construction of numerical methods for the approximate solution of the Schrödinger equation ⋮ High order multistep methods with improved phase-lag characteristics for the integration of the Schrödinger equation ⋮ A new two-step hybrid method 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 hybrid method with phase-lag and derivatives equal to zero for the numerical integration of the Schrödinger equation ⋮ Two-step high order hybrid explicit method for the numerical solution of the Schrödinger equation ⋮ Four step methods for \(y=f(x,y)\) ⋮ A family of eight-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation ⋮ A family of trigonometrically fitted partitioned Runge-Kutta symplectic methods ⋮ A new Numerov-type method for the numerical solution of the Schrödinger equation ⋮ A family of Runge-Kutta methods with zero phase-lag and derivatives for the numerical solution of the Schrödinger equation and related problems ⋮ High order phase fitted multistep integrators for the Schrödinger equation with improved frequency tolerance

Cites Work

• Unnamed Item
• A four-step method for the numerical solution of the 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 sixth-order exponentially fitted method for the numerical solution of the radial Schrödinger equation
• Some New Four-Step Exponential-Fitting Methods for the Numerical Solution of the Radical Schrödinger Equation

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