solving an ODE with a constraint equation

Hi all,

I wondered if there is a numerical solver in MATLAB that can be used to solve this ODE with a constraint:

dy/dx = a/x;

y(0) = 0;

y dx = 1.

"y" is a function of "x", and "a" is an unknow constant that also needs to be solved.

It seems that this is a combination of ODE and an nonlinear equation, and is there any way that I can solve both simutaneously? Thank you.

[Tong Bo]

The example here is only a simple case and I can easily get a analytical solution. But is there a numerical solver that can solve this class of problems?

Answer 1

[Torsten]

As you said: You will have to couple a nonlinear solver with an ODE integrator.

I changed the ODE to dy/dx = a*x because of the singularity of your ODE at x=0.

a0 = 1;
a = fzero(@fun,a0)
% Check
res = fun(a)

function res = fun(a)
  xstart = 0.0;
  xend = 1.0;
  fun = @(x,y) [a*x;y(1)];
  xspan = [xstart,xend];
  y0 = [0;0];
  [t,y] = ode45(fun,xspan,y0);
  res = y(end,2) - 1.0;
end

[Tong Bo]

Thank you for helping with this. Problem solved!

Answer 2

[Walter Roberson]

Typically this would be solved as a Boundary Value Problem, such as bvp4c() or bvp5c()

[Tong Bo]

Thank you for this reply.