the Euler method
First-order accurate:
Click here for euler_step.m.
Click here for f.m.
Click here to see the code in action and to do a graphical convergence study.
Click here to download the script that will do the above graphical convergence study.
Second-order accurate (via Richardson extrapolation):
Click here for richardson_extrap_euler_step_2.m.
Third-order accurate (via Richardson extrapolation):
Click here for richardson_extrap_euler_step_3.m.
the Taylor method
Second-order accurate:
Click here for taylor_2.m
Click here for f.m.
Click here for df.m.
the Runge-Kutta method
Second-order accurate:
Click here for runge_kutta_2.m.
Fourth-order accurate:
Click here for runge_kutta_4.m.
Click here for f.m.
the Adams-Bashforth method
Second-order accurate:
Click here for adams_bashforth_2.m.
Third-order accurate:
Click here for adams_bashforth_3.m.
Fourth-order accurate:
Click here for adams_bashforth_4.m.
Click here for f.m.
the Adams-Moulton method
Second-order accurate:
Click here for adams_moulton_2.m
which does a second-order
predictor corrector based on second-order Runge-Kutta and
Crank-Nicolson.
Click here for f.m.
A matlab *.m file "sys_runge_kutta_2.m" which needs subroutine F_sys.m
Click here for sys_runge_kutta_2.m.
Click here for F_sys.m.