how to solve differential equations

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UGO mela
UGO mela 2016-7-25
评论： UGO mela 2016-7-27
Hi, I'm trying to solve these differential equations with ode45, but i I don't understand how to enter the boundary conditions.
Th,in end tc,in are constant
Could you help me about it? Thank you
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Torsten
Torsten 2016-7-26
solinit = bvpinit(linspace(0,L,100),[Th_in Tc_in Th_in Tc_in Th_in Tc_in Th_in Tc_in Th_in Tc_in]);
Best wishes
Torsten.
UGO mela
UGO mela 2016-7-26
编辑：UGO mela 2016-7-26
I would like to know if I set good function . I set equal 1 all terms W, U, c1.... that are constant except T
Tc_in=5;
Th_in=20;
function dydx=exlode(x,T)
dydx=[(T(2)-T(1)
T(1)+T(3)-2*T(2)
-(T(2)+T(4)-2*T(3))
-(T(3)+T(5)-2*T(4))
T(4)+T(6)-2*T(5)
T(5)+T(7)-2*T(6)
-(T(6)+T(8)-2*T(7))
-(T(7)+T(9)-2*T(8))
T(8)+T(10)-2*T(9)
T(9)-T(10)];
function res=ex1bc(T0,TL)
res=[T0(1)-20 %Tc=20
T0(2)-5 %Tf=5
TL(3)-TL(1)
TL(4)-TL(2)
T0(5)-T0(3)
T0(6)-TL(4)
TL(7)-TL(5)
TL(8)-TL(6)
T0(9)-T0(7)
T0(10)-T0(8)];
solinit = bvpinit(linspace(0,L,100),[Th_in Tc_in Th_in Tc_in Th_in Tc_in Th_in Tc_in Th_in Tc_in]);
sol = bvp4c(@ex1ode,@ex1bc,solinit);
Thank you

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回答（1 个）

Torsten
Torsten 2016-7-26
function main
L=...;
Th_in = 20;
Tc_in = 5;
solinit = bvpinit(linspace(0,L,100),),[Th_in Tc_in Th_in Tc_in Th_in Tc_in Th_in Tc_in Th_in Tc_in]);
sol=bvp4c(@ex1ode,@(T0,TL)ex1bc(T0,TL,Th_in,Tc_in),solinit);
function dydx=exlode(x,T)
dydx=[(T(2)-T(1)
T(1)+T(3)-2*T(2)
-(T(2)+T(4)-2*T(3))
-(T(3)+T(5)-2*T(4))
T(4)+T(6)-2*T(5)
T(5)+T(7)-2*T(6)
-(T(6)+T(8)-2*T(7))
-(T(7)+T(9)-2*T(8))
T(8)+T(10)-2*T(9)
T(9)-T(10)];
function res=ex1bc(T0,TL,Th_in,Tc_in)
res=[T0(1)-Th_in
T0(2)-Tc_in
TL(3)-TL(1)
TL(4)-TL(2)
T0(5)-T0(3)
T0(6)-TL(4)
TL(7)-TL(5)
TL(8)-TL(6)
T0(9)-T0(7)
T0(10)-T0(8)];
Best wishes
Torsten.
  5 个评论
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Torsten
Torsten 2016-7-27
This is an initial-value problem.
Use ODE45 instead of BVP4C to solve
dT/dx = -N*U/L * T^2 T(x=0) = 40
( Solution is T(x)=1/(1/40+N*U/L * x) )
Best wishes
Torsten.
UGO mela
UGO mela 2016-7-27
Sorry for my questions, but I use recently Matlab. When I solved the first system of equations , I plotted the results and I found a strange result on the last T ( 10 ) . All functions with index even T(2), T(4).... are growing except the last T (10) . Could it be link to the function?
The first part of the graphic is link to the odd index [T(1), T(3)..] the second part is link to the even index [T(2), T(4)...]

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