Comparison of some special optimized fourth-order Runge–Kutta methods for the numerical solution of the Schrödinger equation

Modified two‐step hybrid methods for the numerical integration of oscillatory problems

“…In this work, we consider modified TSH methods with frequency dependent coefficients so that the harmonic oscillator is integrated exactly. This approach has been used for Numerov‐type methods and was introduced by Simos in the framework of Runge–Kutta methods , and also applied to the construction of Runge–Kutta‐Nystrom methods . In Section 2, we give a short survey of TSH methods.…”

Approximate analytical versus numerical solutions of Schrödinger equation under molecular Hua potential

“…Some numerical methodologies have been used to solve differential equations of mathematical physics including 1/ N expansion,1, 2 finite element,3, 4 homotopy analysis,5, 6 multipole,7 Runge–Kutta techniques,8, 9 and so forth. Although these techniques are completely reliable, they have their own complexity and cumbersomeness.…”

Out-of-equilibrium dynamics in real band structures

“…is the most commonly used general purpose time stepping algorithm given that it combines ease of implementation, su cient stability, good computational cost, a good order of convergence, and usually performs su ciently well on a very large class of problems [44,45,46]. However, before choosing a time propagation scheme we must consider two important aspects of the behaviour of the Once the simulation diverges we must scrap it completely and restart it with an altered time step.…”