An eighth-order formula for the numerical integration of the one- dimensional Schrödinger equation

DOI10.1016/0021-9991(91)90047-OzbMath0753.65064MaRDI QIDQ1181939

A. C. Allison, A. D. Raptis, Theodore E. Simos

Publication date: 27 June 1992

Published in: Journal of Computational Physics (Search for Journal in Brave)

zbMATH Keywords

performanceeigenvalue problemresonanceradial Schrödinger equationNumerov's methodPhase shifteight order, two-step method

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Finite difference and finite volume methods for ordinary differential equations (65L12) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items

Arbitrarily precise numerical solutions of the one-dimensional Schrödinger equation, A TWELFTH-ORDER FOUR-STEP FORMULA FOR THE NUMERICAL INTEGRATION OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION, 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, On an eighth order formula for solving a Schrödinger equation, High Algebraic Order Methods for the Numerical Solution of the Schrödinger Equation

Cites Work

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• Exponential and Bessel fitting methods for the numerical solution of the Schrödinger equation
• On the numerical solution of Schrödinger's radial equation
• Comparison of some four-step methods for the numerical solution of the Schrödinger equation
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• A finite difference approach for the calculation of perturbed oscillator energies
• On the interaction of the type λx2/(1+g x2)
• Symmetric Multistip Methods for Periodic Initial Value Problems
• Rayleigh-Schrodinger perturbation theory with a strong perturbation: anharmonic oscillators
• An Improved Eigenvalue Corrector Formula for Solving the Schrodinger Equation for Central Fields