Capitolul 1 Ecuatii diferentiale de ordinul ˆıntâi rezolvabile prin ...

Calculul simbolic ¸si numeric pentru ecuat¸ii parabolice 251
Exemplul 2:
⎧
⎪⎨
⎪⎩
∂u
(x, t) = 4
∂t
Figura 31
∂ 2 u
∂x 2
u(0, t) = u(π, t) = 0
u(x, 0) = 4 cosxsin x
(x, t) + e −4t · sin x
Heat equation
> PDE2 :=
diff(u(x,t),t)=4*diff(u(x,t),x,x)+(exp(-4*t))*sin(x);
PDE2 := ∂
∂t
u (x, t) = 4 ∂2
∂x 2u (x, t) + e −4 t sin (x)
> IBC2 := {u(0,t)=0,u(Pi,t)=0,u(x,0)=4*cos(x)*sin(x)};
IBC2 := {u (0, t) = 0, u (π, t) = 0, u (x, 0) = 4 cos (x) sin (x)}
> pds2 := pdsolve(PDE2,IBC2,numeric);
pds1 := module () local INFO; export plot, plot3d, animate,
value, settings; option ‘Copyright (c) 2001 by Waterloo
Maple Inc. All rights reserved.‘; end module
> p6 := pds2:-plot(t=0):
p7 := pds2:-plot(t=1/10):