Contact Us!
CoCalc Logo Icon
StoreFeaturesDocsShareSupportNewsAboutSign UpSign In

Real-time collaboration for Jupyter Notebooks, Linux Terminals, LaTeX, VS Code, R IDE, and more,
all in one place. Commercial Alternative to JupyterHub.

| Download
Views: 97
Image: ubuntu2004
Tweet
Share
Share
Kernel: SageMath 9.7
x,t=var('x, t')
T=function('T')(x,t)
k_per = 1.7
rho_per=1
Cp_per =4186
#Définir l'équation de la chaleur
equ_chal = diff(T,t)*rho_per*Cp_per - diff(T,x,2)*k_per==0
#recherher les solutions analystiques de l'équation différencielle
#sol = desolve(equ_chal, [x,t]); sol
#conditions aux limites 
sol0=desolve(equ_chal,[x,t],ics=[0,0]);print(sol0)
sol1=desolve(equ_chal,[x,t],ics=[0,1]);print(sol1)
sol2=desolve(equ_chal,[x,t],ics=[0,2]);print(sol2)
# tracer
sol=desolve(equ_chal,[x,t],ics=[0,0]); sol
plot(sol.substitute(r==0.5) ,(0,0))
--------------------------------------------------------------------------- NotImplementedError Traceback (most recent call last) Input In [4], in <cell line: 11>() 7 equ_chal = diff(T,t)*rho_per*Cp_per - diff(T,x,Integer(2))*k_per==Integer(0) 8 #recherher les solutions analystiques de l'équation différencielle 9 #sol = desolve(equ_chal, [x,t]); sol 10 #conditions aux limites ---> 11 sol0=desolve(equ_chal,[x,t],ics=[Integer(0),Integer(0)]);print(sol0) 12 sol1=desolve(equ_chal,[x,t],ics=[Integer(0),Integer(1)]);print(sol1) 13 sol2=desolve(equ_chal,[x,t],ics=[Integer(0),Integer(2)]);print(sol2)
File /ext/sage/9.7/src/sage/calculus/desolvers.py:598, in desolve(de, dvar, ics, ivar, show_method, contrib_ode, algorithm) 596 raise NotImplementedError("Maxima was unable to solve this ODE.") 597 else: --> 598 raise NotImplementedError("Maxima was unable to solve this ODE. Consider to set option contrib_ode to True.") 600 if show_method: 601 maxima_method=P("method")
NotImplementedError: Maxima was unable to solve this ODE. Consider to set option contrib_ode to True. 
equ_chal = diff(T,t)*rho_per*Cp_per - diff(T,x,2)*k_per

solve (equ_chal,[x,t])
[]
x,t=var('x,t')
T=function('T')(x,t)
k_per = 1.7
rho_per=1
Cp_per =4186

ed= diff(T,t)*rho_per*Cp_per - diff(T,x,2)*k_per

desolve (ed,[x,t],ics=[5,10,-5],contrib_ode=True)
--------------------------------------------------------------------------- NotImplementedError Traceback (most recent call last) Input In [44], in <cell line: 9>() 5 Cp_per =Integer(4186) 7 ed= diff(T,t)*rho_per*Cp_per - diff(T,x,Integer(2))*k_per ----> 9 desolve (ed,[x,t],ics=[Integer(5),Integer(10),-Integer(5)],contrib_ode=True)
File /ext/sage/9.7/src/sage/calculus/desolvers.py:596, in desolve(de, dvar, ics, ivar, show_method, contrib_ode, algorithm) 594 soln = P(cmd) 595 if str(soln).strip() == 'false': --> 596 raise NotImplementedError("Maxima was unable to solve this ODE.") 597 else: 598 raise NotImplementedError("Maxima was unable to solve this ODE. Consider to set option contrib_ode to True.")
NotImplementedError: Maxima was unable to solve this ODE. 
#Résoudre l'équation de la chaleur avec T(x,t) qui prend la forme : T(x,t)=f(x)*g(t)

x,t=var('x,t')
k_per = 1.7
rho_per=1
Cp_per =4186
D = k_per/(rho_per*Cp_per)

f=function('f')(x)
g=function('g')(t)
T= f*g
eq(x,t) = D*diff(T,x,2) == diff (T,t)
eq (x,t)
0.000406115623506928*g(t)*diff(f(x), x, x) == f(x)*diff(g(t), t)
#obtenir une équation où chaque coté dépend d'une seule variable : que du x à gauche et que du t à droite
eqn = eq/T
eqn(x,t)
0.000406115623506928*diff(f(x), x, x)/f(x) == diff(g(t), t)/g(t)
#
k=var('k')
eq1(x,t)=eqn(x,t).lhs() == k
eq2(x,t)=eqn(x,t).rhs() == k

#solution de g
g(t)=desolve(eq2(x,t),[g,t])
g(t)
_C*e^(k*t)
#solution de f ->k doit etre >0:
période == 24*6*30
w==2*pi/période
assume (k>0)
f(x)=desolve(eq1(x,t),[f,x])
f(x)
_K1*e^(2/17*sqrt(10465)*sqrt(17)*sqrt(k)*x) + _K2*e^(-2/17*sqrt(10465)*sqrt(17)*sqrt(k)*x)
# Solution finale : T(x,t)=f(x)*g(t)
T(x,t)=g*f
période == 24*6*30
w==2*pi/période
T= desolve(T(x,t),[x,t],T(0,t)==sin(w*t))
plot(T(x,t))
--------------------------------------------------------------------------- NotImplementedError Traceback (most recent call last) Input In [30], in <cell line: 5>() 3 période == Integer(24)*Integer(6)*Integer(30) 4 w==Integer(2)*pi/période ----> 5 T= desolve(T(x,t),[x,t],T(Integer(0),t)==sin(w*t)) 6 plot(T(x,t))
File /ext/sage/9.7/src/sage/calculus/desolvers.py:598, in desolve(de, dvar, ics, ivar, show_method, contrib_ode, algorithm) 596 raise NotImplementedError("Maxima was unable to solve this ODE.") 597 else: --> 598 raise NotImplementedError("Maxima was unable to solve this ODE. Consider to set option contrib_ode to True.") 600 if show_method: 601 maxima_method=P("method")
NotImplementedError: Maxima was unable to solve this ODE. Consider to set option contrib_ode to True. 
# on définit le CL et CI pour trouver les constantes 
période == 24*6*30
w==2*pi/période
T(0,t)==5*sin(wt)
T(x,0)==-1
T(x,t)
--------------------------------------------------------------------------- TypeError Traceback (most recent call last) Input In [14], in <cell line: 4>() 2 période = Integer(24)*Integer(6)*Integer(30) 3 w=Integer(2)*pi/période ----> 4 T(Integer(0),t)==Integer(5)*sin(wt) 5 T(x,Integer(0))==-Integer(1) 6 T(x,t)
File /ext/sage/9.7/src/sage/symbolic/expression.pyx:6182, in sage.symbolic.expression.Expression.__call__() 6180 z^2 + x^y 6181 """ -> 6182 return self._parent._call_element_(self, *args, **kwds) 6183 6184 def variables(self):
File /ext/sage/9.7/src/sage/symbolic/ring.pyx:1047, in sage.symbolic.ring.SymbolicRing._call_element_() 1045 d = args[0] 1046 else: -> 1047 raise TypeError("Substitution using function-call syntax " 1048 "and unnamed arguments has been removed. You " 1049 "can use named arguments instead, like "
TypeError: Substitution using function-call syntax and unnamed arguments has been removed. You can use named arguments instead, like EXPR(x=..., y=...) 
#Graph:
plot(T(x,t))
--------------------------------------------------------------------------- TypeError Traceback (most recent call last) Input In [20], in <cell line: 2>() 1 #Graph: ----> 2 plot(T(x,t))
File /ext/sage/9.7/src/sage/symbolic/expression.pyx:6182, in sage.symbolic.expression.Expression.__call__() 6180 z^2 + x^y 6181 """ -> 6182 return self._parent._call_element_(self, *args, **kwds) 6183 6184 def variables(self):
File /ext/sage/9.7/src/sage/symbolic/ring.pyx:1047, in sage.symbolic.ring.SymbolicRing._call_element_() 1045 d = args[0] 1046 else: -> 1047 raise TypeError("Substitution using function-call syntax " 1048 "and unnamed arguments has been removed. You " 1049 "can use named arguments instead, like "
TypeError: Substitution using function-call syntax and unnamed arguments has been removed. You can use named arguments instead, like EXPR(x=..., y=...)