I have a coupled second order DE; how to solve them with boundary conditions; How to get get F1 and F2

equation 1: d^2f1/dx^2-Q/K1*F1+P/K1=0

equation 2 d^2f2/dx^2-Q/K1*F2+P/K2=0 Boundary conditions F1(0)=0 F2(l)=P F1(l-u)=F2(l-u) dF1/dx(l-u)=dF2/dx(l-u) PS All variables l, u, P,Q and K1 are known

Answer 1

[Torsten]

Use "bvp4c" with the "multipoint boundary value problem" facility:

https://de.mathworks.com/help/matlab/ref/bvp4c.html#bt5uooc-23

https://de.mathworks.com/help/matlab/math/boundary-value-problems.html#brfhdsd-1

Best wishes

Torsten.

[Nadim Mhanna]

How to put the boundary the last boundary condition

[Torsten]

function dydx = f(x,y,region)
     P = ...;
     Q = ...;
     K1 = ...;
     K2 = ...;

     dydx = zeros(2,1);
     dydx(1) = y(2);

     % The definition of dydx(2) depends on the region.
     switch region
        case 1                                % x in [0 l-u]
     dydx(2) = y(1)*Q/K1-P/K1
        case 2                                % x in [l-u l]
         dydx(2) = y(1)*Q/K1-P/K2; 
      end

function res = bc(YL,YR)
   P=...;
   res = [YL(1,1)               % y(0) = 0
          YR(1,1) - YL(1,2)     % Continuity of F(x) at x=l-u
          YR(2,1) - YL(2,2)     % Continuity of dF/dx at x=l-u
          YR(1,end) - P];       % y(l) = P

You should be able to add initial conditions and call "bvp4c" following the example in my above link.

Of course, you will have to give values to the parameters used in the function routines.

Best wishes

Torsten.