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matlabdifferential-equations

Bvp4c with unknown boundary

I have a BVP describing the sagging of a catenary, where the right boundary is unknown (8 DE and 9 BC). Does anybody know how to model this in Matlab with the function bvp4c? Thank you.

Solution

  • The same method as in the linked post applies, if you have a function right_side(t,x) and boundary_conditions(xa,xb) then you need wrapper functions that handle the additional component for the interval length,

    function doty = wrapper_rhs(s,y)
  T = y(end)
  doty = T*right_side(t0+s*T, y(1:end-1))
  doty(end+1)=0
end

    and 

    function bc = wrapper_bc(ya,yb)
  bc = boundary_conditions(ya(1:end-1), yb(1:end-1))
end

    These should allow to call the BVP solver over the fixed interval ´[0,1]´.