BVP4c Solving two equations simultaneously

Say for example I have an 4th order ODE

y''' = A*y''+y

on the boundary [0 1] with the BC

y(0) = 1; y'(0) = 0; y(1) = 2; y'(1) = 0

I have my code setup like this.

init = bvpinit(linspace(0,1,10),[0,0,0,0]);
sol = bvp4c(@rhs_bvp, @bc_bvp, init);
x1 = linspace(0,1,100);
BS = deval(sol, x1);

function [ rhs ] = rhs_bvp( x, y )
A = 10;
rhs = [y(2); 
       y(3);
       y(4);
       A*y(3)+y(1)];
end

function [ bc ] = bc_bvp( yl, yr)
bc = [yl(1) - hi; 
      yl(2);
      yr(1) - ho;
      yr(2)];
end

Now Say I want to add another equation to solve simultaneously

V' = y

on the same boundary with BC

V(0) = 0; V(1) = 1

How would I go about including this new equation into this solver?

[David Goodmanson]

Hi Taylor,

If you start with (your original expression was a typo)

y'''' = A*y''+ y

and plug in y = V', you obtain a fifth order differential equation. But now you have six boundary conditions,which appears to be one too many.

Answer 1

[Torsten]

init = bvpinit(linspace(0,1,10),[0,0,0,0,0]);
sol = bvp4c(@rhs_bvp, @bc_bvp, init);
x1 = linspace(0,1,100);
BS = deval(sol, x1);

function [ rhs ] = rhs_bvp( x, y )
A = 10;
rhs = [y(2); 
       y(3);
       y(4);
       A*y(3)+y(1);
       y(1)];
end

function [ bc ] = bc_bvp( yl, yr)
bc = [yl(1) - hi; 
      yl(2);
      yr(1) - ho;
      yr(2)
      yl(5)];
  %or yr(5)-1.0];
end