ERROR USING A FUNCTION INSIDE ODE FUNCTION

I am trying to solve a 2nd order differential equation which involves invoking a function defined in the main code from inside another function. However, I am ending up with an error that says

    Undefined function or variable 'partial_psi_x'.

    Error in P3>odefunc (line 103)
    dudt = -partial_psi_x(x,y,z);

    Error in odearguments (line 90)
    f0 = feval(ode,t0,y0,args{:});   % ODE15I sets args{1} to yp0.

    Error in ode45 (line 115)
    odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

    Error in P3 (line 91)
    [t,s] = ode45(@odefunc, tspan, s0);

Relevant piece of code is as follows:

    partial_psi_x = partial_psi_b_x + partial_psi_d_x + partial_psi_h_x;
    partial_psi_y = partial_psi_b_y + partial_psi_d_y + partial_psi_h_y;
    partial_psi_z = partial_psi_b_z + partial_psi_d_z + partial_psi_h_z;

    partial_psi_x = matlabFunction(partial_psi_x);
    partial_psi_y = matlabFunction(partial_psi_y);
    partial_psi_z = matlabFunction(partial_psi_z);

   % ODE
   tstart = 0;
   tstop = 2*pi;
   tspan=tstart:tstop;
   s0=[-R0;0;0;0;V0;0];
   [t,s] = ode45(@odefunc, tspan, s0);

   function dsdt = odefunc(t,s)
   x = s(1);
   y = s(2);
   z = s(3);
   u = s(4);
   v = s(5);
   w = s(6);
   dxdt = u;
   dydt = v;
   dzdt = w;
   dudt = -partial_psi_x(x,y,z);
   dvdt = -partial_psi_y(x,y,z);
   dwdt = -partial_psi_z(x,y,z);
   dsdt = [dxdt;dydt;dzdt;dudt;dvdt;dwdt];
   end

where partial_psi_x, partial_psi_y and partial_psi_z are function handles (after using MatlabFunction) to partial derivatives of a function psi in terms of x, y and z. I have checked until the point of obtaining the three function handles and they seem to work without any issues. However, when I try to access these functions from inside odefunc, I get error as mentioned above. I am fairly new to numerical integration technique in MATLAB but have tried to look up a similar approach of using functions inside an ode solver but could not find any solution. Any help on the issue will be highly appreciated.

Answer 1

[Walter Roberson]

You should pass in those function handles as extra parameters.

http://www.mathworks.com/help/matlab/math/parameterizing-functions.html

[Sam]

I did replace the function dsdt with:

 function dsdt = 
odefunc(t,s,partial_psi_x,
partial_psi_y,partial_psi_z)

and ending up with error :

Not enough input arguments.
Error in P3 (line 91)
[t,s] = ode45(@odefunc, tspan, s0);

[Walter Roberson]

    partial_psi_x = partial_psi_b_x + partial_psi_d_x + partial_psi_h_x;
    partial_psi_y = partial_psi_b_y + partial_psi_d_y + partial_psi_h_y;
    partial_psi_z = partial_psi_b_z + partial_psi_d_z + partial_psi_h_z;

    partial_psi_x = matlabFunction(partial_psi_x);
    partial_psi_y = matlabFunction(partial_psi_y);
    partial_psi_z = matlabFunction(partial_psi_z);

   % ODE
   tstart = 0;
   tstop = 2*pi;
   tspan=tstart:tstop;
   s0=[-R0;0;0;0;V0;0];
   [t,s] = ode45(@(t,s) odefunc(t, s, partial_psi_x, partial_psi_y, partial_psi_z), tspan, s0);

   function dsdt = odefunc(t, s,partial_psi_x, partial_psi_y, partial_psi_z)
   x = s(1);
   y = s(2);
   z = s(3);
   u = s(4);
   v = s(5);
   w = s(6);
   dxdt = u;
   dydt = v;
   dzdt = w;
   dudt = -partial_psi_x(x,y,z);
   dvdt = -partial_psi_y(x,y,z);
   dwdt = -partial_psi_z(x,y,z);
   dsdt = [dxdt;dydt;dzdt;dudt;dvdt;dwdt];
   end

[Sam]

Thanks! this works, but may I ask why the function handles haven't been included in the argument list after @?

[Walter Roberson]

They were included. ode45 is being passed multiple arguments, the first of which is

   @(t,s) odefunc(t, s, partial_psi_x, partial_psi_y, partial_psi_z)

This constructs an anonymous function that takes two arguments. The action of the anonymous function is to call odefunc with 5 arguments.