odes_runge_kutta

odes_runge_kutta, considers the approximate solution of an ordinary differential equation (ODE) using a Runge-Kutta method.

The notes:

• odes_runge_kutta.pdf
• odes_runge_kutta.tex

Scripts and functions:

• border_plot.m, draws the stability boundary for the AB2 ODE solver, (y(n+1)-y(n))/dt = lambda * ( 3/2 yn - 1/2 yn-1).
• expsin_exact.m, evaluates the exact solution of the expsin test problem.
• expsin_prime.m, the right hand side of the expsin test problem.

Images:

• border_plot.png, a plot of the stability boundary for the AB2 ODE solver, (y(n+1)-y(n))/dt = lambda * ( 3/2 yn - 1/2 yn-1).
• runge_kutta.png, a diagram suggesting the intermediate computations in a fourth-order Runge-Kutta step.