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

Calculul simbolic ¸si numeric pentru ecuat¸ii parabolice 253
Exemplul 3:
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∂u
∂t (x, t) = ∂2u ∂x2(x, t) + t · cosx
u(0, t) = t, u(π, t) = 0
u(x, 0) = cos 2x + cos 3x
Heat equation
> PDE3 :=
diff(u(x,t),t)=diff(u(x,t),x,x)+t*cos(x);
PDE3 := ∂
∂t
u (x, t) = ∂2
∂x 2u (x, t) + t cos (x)
> IBC3 := {u(0,t)=t,u(Pi,t)=0,u(x,0)=cos(2*x)+cos(3*x)};
IBC3 := {u (π, t) = 0, u (0, t) = t, u (x, 0) = cos (2 x) + cos (3 x)}
> pds3 := pdsolve(PDE3,IBC3,numeric);
pds1 := module () local INFO; export plot, plot3d, animate,
value, settings; option ‘Copyright (c) 2001 by Waterloo
Maple Inc. All rights reserved.‘; end module
> q1 := pds3:-plot(t=0):
q2 := pds3:-plot(t=1/10):
q3 := pds3:-plot(t=1/2):
q4 := pds3:-plot(t=1):
q5 := pds3:-plot(t=2):
plots[display]({q1,pq2,q3,q4,q5},
title=‘Heat profile at t=0,0.1,0.5,1,2‘);