how to solve differential equations

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

[Star Strider]

Use bvp4c or bvp5c for boundary value problems.

[UGO mela]

Thanks for your reply I can not understand how to determine the term solinit of the function.

[Torsten]

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]

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

Answer 1

[Torsten]

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.

[UGO mela]

How does the function become if I have only the first equation?

Thank you Ugo

[Torsten]

But - as it stands - you can't solve the first equation without solving the second equation, too ...

Best wishes

Torsten.

[UGO mela]

I would like to include this equation with the same function.

How can I do? Thank you

[Torsten]

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]

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)...]