How to add "erf()" part to the ode solution?
1 vue (au cours des 30 derniers jours)
Afficher commentaires plus anciens
Hi,
I have the ODE : y' = -x+2+10*e^(10*(x-1)^2)
I have numeric solution of below:
I have a analytical solution of ODE below:
y (x)= C1 + 2*x - x^2/2 + (10^(1/2)*pi^(1/2)*erfi(10^(1/2)*(x - 1)))/2, y(0)=1
when I plot the analytical solution without "erfi()" part, the graph is below:
The curve is similar to numarical solution but there is evident error. I think, this error is because of "erf" part of the analytical solution. How can I plot the analytical solution with the "erf()" part. Thank you.
0 commentaires
Réponse acceptée
Torsten
le 19 Oct 2022
Modifié(e) : Torsten
le 19 Oct 2022
syms x y(x)
eqn = diff(y,x) - (-x+2+10*exp(-10*(x-1)^2)) == 0;
cond = y(0)==1;
sol = dsolve(eqn,cond)
fplot(sol,[0 6])
3 commentaires
Les Beckham
le 19 Oct 2022
Without the symbolic toolbox:
x = linspace(0, 6, 1000);
rt = sqrt(10);
rp = sqrt(pi);
y = 2*x - x.^2/2 + (rt*rp*erf(rt))/2 + (rt*rp*erf(rt*(x-1)))/2 + 1;
plot(x,y)
grid on
Plus de réponses (0)
Voir également
Catégories
En savoir plus sur Calculus dans Help Center et File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!