I have been given question that I could only half answer:
consider a one step method for an ODE
yi+1 = yi + h/4 (f(ti,yi)+3f(ti + (2h/3), yi + (2h/3)f(ti,yi))
1) find the inequality which must be satisfied by the step size h such that the method will be stable for the ODE dy/dt = -lambda*y
2) plot the stability region z = h*lambda
I have managed to do 1) by solving for dy/dt = -lambda*y, but am unable to plot the stability region. Please can any some one help:
The answer I got to 1) is : abs(1-h*lambda+0.5(h*lambda)^2) < 1. so substituing for
z = lambda*y I got,
abs(1-z+0.5*z^2) < 1 in the complex plane.
Thank you.
dinner.