A TWELFTH-ORDER FOUR-STEP FORMULA FOR THE NUMERICAL INTEGRATION OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION

DOI10.1142/S0129183103005194zbMath1079.81018MaRDI QIDQ5699953

Yongming Dai, Zhongcheng Wang

Publication date: 27 October 2005

Published in: International Journal of Modern Physics C (Search for Journal in Brave)

zbMATH Keywords

Schrödinger equationeigenvalue problemshigh precision methodshigh-order linear four-step methodsMulti-derivative

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) Computational methods for problems pertaining to quantum theory (81-08)

Related Items (9)

Arbitrarily precise numerical solutions of the one-dimensional Schrödinger equation ⋮ Exponentially fitted multi-derivative linear methods for the resonant state of the Schrödinger equation ⋮ An improved trigonometrically fitted P-stable Obrechkoff method for periodic initial-value problems ⋮ A Mathematica program for the two-step twelfth-order method with multi-derivative for the numerical solution of a one-dimensional Schrödinger equation ⋮ A new effective algorithm for the resonant state of a Schrödinger equation ⋮ A trigonometrically-fitted one-step method with multi-derivative for the numerical solution to the one-dimensional Schrödinger equation ⋮ P-stable linear symmetric multistep methods for periodic initial-value problems ⋮ A new kind of high-efficient and high-accurate P-stable Obrechkoff three-step method for periodic initial-value problems ⋮ A four-step trigonometric fitted P-stable Obrechkoff method for periodic initial-value problems

Cites Work

• A 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
• An eighth-order formula for the numerical integration of the one- dimensional Schrödinger equation
• P-stable exponentially fitted methods for the numerical integration of the Schrödinger equation
• Embedded methods for the numerical solution of the Schrödinger equation
• Practical points concerning the solution of the Schrödinger equation
• The numerical solution of coupled differential equations arising from the Schrödinger equation
• Symmetric Multistip Methods for Periodic Initial Value Problems
• A P-stable complete in phase Obrechkoff trigonometric fitted method for periodic initial-value problems

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