Integral approximation with midpoint method

13 visualizzazioni (ultimi 30 giorni)
Dana Chica
Dana Chica il 13 Mar 2017
I want to write a code for the Integral approximation with the midpoint method.
Mathematically, I was thinking like this: y'(t)=f(t,y(t))=-y(t)
The rectangle rule: y(t + h)=y(t) + h · f(t+h/2,y(t)+h/2*f(t,y(t)))
for:
h=0.5 and y(0)=1 (t0=0, y(t0)=1)
I would like to calculate the next step: t1=t0+h=0.5, y(t1)=?
y(t1)=y(t0+h)=y(t0)+h*f(t0+h/2,y(t0)+h/2*f(t0,y(t0)))=
=1+0.5*f(0.25,1+0.25*f(0,1))=
=1+0.5*f(0.25,1+0.25*(-1))=
=1+0.5*f(0.25,0.75) = 1+0.5*(-0.75)=0.625
I don't know how to represent the function f in Matlab (syms ?) so that it would know to calculate f(0,1) for example.
Can someone help me, please?

Risposte (0)

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by