High order computationally economical six-step method with vanished phase-lag and its derivatives for the numerical solution of the Schrödinger equation

DOI10.1007/s10910-016-0714-8zbMath1383.65078OpenAlexW2561605061MaRDI QIDQ683854

Dmitriy B. Berg, Theodore E. Simos

Publication date: 9 February 2018

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-016-0714-8

zbMATH Keywords

algorithmstabilitynumerical exampleSchrödinger equationphase-lagcomputational efficiencymultistep methodstruncation errorderivatives of the phase-laginterval of periodicitymultistage methodsphase-fitted

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Stability and convergence of numerical methods for ordinary differential equations (65L20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Complexity and performance of numerical algorithms (65Y20) Linear boundary value problems for ordinary differential equations (34B05)

Related Items (10)

New three-stages symmetric six-step finite difference method with vanished phase-lag and its derivatives up to sixth derivative for second order initial and/or boundary value problems with periodical and/or oscillating solutions ⋮ A new six-step algorithm with improved properties for the numerical solution of second order initial and/or boundary value problems ⋮ A new three-stages six-step finite difference pair with optimal phase properties for second order initial and/or boundary value problems with periodical and/or oscillating solutions ⋮ Three stages symmetric six-step method with eliminated phase-lag and its derivatives for the solution of the Schrödinger equation ⋮ An efficient six-step method for the solution of the Schrödinger equation ⋮ New multiple stages multistep method with best possible phase properties for second order initial/boundary value problems ⋮ A multistep method with optimal properties for second order differential equations ⋮ New four-stages symmetric six-step method with improved phase properties for second order problems with periodical and/or oscillating solutions ⋮ A new multistep finite difference pair for the Schrödinger equation and related problems ⋮ Algorithm for the development of families of numerical methods based on phase-lag Taylor series

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