Finite difference method to solve a nonlinear eqn?
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Onur Metin Mertaslan
on 25 Mar 2022
Commented: Onur Metin Mertaslan
on 25 Mar 2022
Hello,
I have a second order nonlinear question and I need to solve it for different times by using finite difference method but I don't know how to start it. I am quite new in Matlab. Is there anyone who can help me or at least show me a way to do this?
thank you
6 Comments
Torsten
on 25 Mar 2022
g = 9.81;
L = 1.0;
T = 1.0;
dT = 0.01;
y_0 = pi/2;
v_0 = 0;
f = @(t,y)[y(2);-g/L*sin(y(1))];
tspan = 0:dT:T;
y0 = [y_0;v_0];
[t,y] = ode45(f,tspan,y0);
plot(t,y)
Accepted Answer
Torsten
on 25 Mar 2022
Edited: Torsten
on 25 Mar 2022
g = 9.81;
L = 1.0;
T = 1.0;
dT = 0.01;
y_0 = pi/2;
v_0 = 0;
f = @(t,y)[y(2);-g/L*sin(y(1))];
tspan = 0:dT:T;
y0 = [y_0;v_0];
[t,y] = ode45(f,tspan,y0);
y_linear = v_0/sqrt(g/L)*sin(sqrt(g/L)*t) + y_0*cos(sqrt(g/L)*t);
plot(t,[y(:,1),y_linear])
3 Comments
Torsten
on 25 Mar 2022
Edited: Torsten
on 25 Mar 2022
The graph won't change because the dt is not the actual stepsize of the solver, but prescribes the output times for ode45. The stepsize is chosen by the solver and computed internally - you can't influence it because it's adaptively chosen and different for each time step to meet a prescribed error tolerance.
If you want a fixed-step solver to solve your equations for which you can prescribe the stepsize, you will have to program it on your own. E.g. explicit Euler is a simple one.
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