1), and we illustrate numerically that it gives more accurate results for long-time simulations than the Runge-Kutta
weak secondorder method; see [11, Chapter 15.
In order to use fourth-order Runge-Kutta
method [58-59] to solve numerically Equation (5) we must further discretize Equations (75) and (76), which can be denoted as
In Section 3, we define the initial value problem and discuss the Runge-Kutta
Heun method of order 3.
Then the resulting differential equations can be integrated using fourth-order Runge-Kutta
The above equation is solved using Runge-Kutta
4th order method.
A common Runge-Kutta
routine could easily out-compute symbolic differential equation solvers in a head-to-head competition.
Solution for the Time-Independent Schrodingcr Equation Using the Runge-Kutta
Using the Runge-Kutta
method as employed by Griffith (ref.
algorithm with adaptive step-size control was used to calculate the trajectories of protons and neutrons .
3) was integrated using a fourth-order Runge-Kutta
method for the given sets of parameters.
Stability regions for Runge-Kutta
and Adams Schemes
We have shown that collocation Runge-Kutta
time-stepping schemes applied to a spatially semi-discretized linear parabolic evolution equation produce a solution that a priori depends continuously on the input data in a parabolic space-time norm, but its operator norm may be large, unless the parabolic CFL number is of order one.