An embedded exponentially-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation and related periodic initial-value problems

DOI10.1016/S0010-4655(00)00080-1zbMath0982.65079OpenAlexW2042907355MaRDI QIDQ1587743

George Avdelas, Jesus Vigo Aguiar, Theodore E. Simos

Publication date: 3 December 2000

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0010-4655(00)00080-1

zbMATH Keywords

numerical resultsperiodic solutionsSchrödinger equationinitial-value problemsoscillating solutionsexponential fittingembedded Runge-Kutta methods

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Nonlinear ordinary differential equations and systems (34A34) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items

Exponentially fitted explicit Runge-Kutta-Nyström methods ⋮ Limit-cycle-preserving simulation of gene regulatory oscillators ⋮ New optimized explicit modified RKN methods for the numerical solution of the Schrödinger equation ⋮ A new class of two-step P-stable TFPL methods for the numerical solution of second-order IVPs with oscillating solutions ⋮ A new modified embedded 5(4) pair of explicit Runge-Kutta methods for the numerical solution of the Schrödinger equation ⋮ On symplectic and symmetric ARKN methods ⋮ Exponential fitted Runge-Kutta methods of collocation type: Fixed or variable knot points? ⋮ A new family of phase-fitted and amplification-fitted Runge-Kutta type methods for oscillators ⋮ Minimum storage Runge-Kutta schemes for computational acoustics. ⋮ An optimized Runge-Kutta method for the numerical solution of the radial Schrödinger equation ⋮ New optimized two-derivative Runge-Kutta type methods for solving the radial Schrödinger equation ⋮ A 5(3) pair of explicit ARKN methods for the numerical integration of perturbed oscillators. ⋮ A new embedded 5(3) pair of modified Runge-Kutta-Nyström methods for the numerical solution of the Schrödinger equation ⋮ AN EMBEDDED 5(4) PAIR OF MODIFIED EXPLICIT RUNGE–KUTTA METHODS FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION ⋮ Exponentially fitted TDRK pairs for the Schrödinger equation ⋮ Piecewise-linearized methods for initial-value problems with oscillating solutions ⋮ Revised trigonometrically fitted two-step hybrid methods with equation dependent coefficients for highly oscillatory problems ⋮ Exponentially fitted multi-derivative linear methods for the resonant state of the Schrödinger equation ⋮ Runge-Kutta-Nyström methods with equation dependent coefficients and reduced phase lag for oscillatory problems ⋮ Trigonometrically fitted two-step Obrechkoff linear methods for the Schrödinger equation ⋮ A new minimum storage Runge-Kutta scheme for computational acoustics ⋮ Modified explicit Runge-Kutta methods for the numerical solution of the Schrödinger equation ⋮ Comparison of some special optimized fourth-order Runge-Kutta methods for the numerical solution of the Schrödinger equation ⋮ Exponentially fitted symplectic integrators of RKN type for solving oscillatory problems ⋮ Two-frequency trigonometrically-fitted and symmetric linear multi-step methods for second-order oscillators ⋮ Optimal implicit exponentially-fitted Runge-Kutta methods ⋮ Obrechkoff two-step method fitted with Fourier spectrum for undamped Duffing equation ⋮ A new approach to solve the Schrodinger equation with an anharmonic sextic potential ⋮ An embedded pair of exponentially fitted explicit Runge-Kutta methods