Implicit Solution with MATLAB
Implicit methods are available for MATLAB, too. We need to prepare an M-file which defines the equation and then call the subroutine (ode15s) to do the integration. This method may seem mysterious at first because you call a subroutine, which in turn calls your M-file. Thus the commands you give and the M-file are somewhat disparate.
For example, one stiff package is called ode15s. To solve the turbulence modelwe would replace the statement
[t,u] = ode45('turb',t0,tend,u0)
with
[t,u] = ode15s('turb',[t0,tend],u0)
If the problem is stiff then such methods may be needed.
Take Home Message: If the initial value problem is stiff, use an implicit method.