SIMPLE AND ACCURATE EXPLICIT BESSEL AND NEUMANN FITTED METHODS FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION

DOI10.1142/S0129183100000080zbMath0946.65052MaRDI QIDQ4488299

Theodore E. Simos

Publication date: 5 July 2000

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

zbMATH Keywords

Schrödinger equationvariable-step algorithmspherical Bessel and Neumann functionsfourth algebraic order methods

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Numerical methods for initial value problems involving ordinary differential equations (65L05) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

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Cites Work

• New variable-step procedure for the numerical integration of the one- dimensional Schrödinger equation
• 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
• Comparison of numerical methods for solving the second-order differential equations of molecular scattering theory
• An explicit almost \(P\)-stable two-step method with phase-lag of order infinity for the numerical integration of second-order periodic initial- value problems
• Piecewise perturbation methods for calculating eigensolutions of a complex optical potential
• Embedded methods for the numerical solution of the Schrödinger equation
• A generator of high-order embedded \(P\)-stable methods for the numerical solution of the Schrödinger equation
• The numerical solution of coupled differential equations arising from the Schrödinger equation
• Solving Nonstiff Ordinary Differential Equations—The State of the Art
• High Algebraic Order Methods with Minimal Phase-Lag for Accurate Solution of the Schrödinger Equation
• An Eighth Order Exponentially Fitted Method for the Numerical Solution of the Schrödinger Equation