While leaving out much of the details, this learning module provides enough information about the algorithm so that readers can write a computer program to perform Runge-Kutta marching.

There are several ODE solvers available in Matlab. One particular solver called “ODE45” ce algorithm. This version simultaneously solves a pair of 4th order and 5th order Runge-Kutta updates. If the …

Running a 2-stage Runge-Kutta method ... the global error is 4.20e-03. Apply the midpoint method (see Exercise 1) to the test equation. Compare the local and global error of the midpoint method to the …

The formulas describing Runge-Kutta methods look the same as those of the collocation methods of the previous chapter, but are abstracted away from the ideas of quadrature and collocation.

Here’s the formula for the Runge-Kutta-Fehlberg method (RK45).

Runge-Kutta methods can be applied to a first order equation or to higher order ordinary differential equations through first resolving them to systems of first order equations.

In contrast to the multistep methods of the previous section, Runge-Kutta methods are single-step methods — however, with multiple stages per step. They are motivated by the dependence of the …