How can I implement the lsqnonlin&lsqcurvefit function to find one parameter of the PDE without knowing the analytical solution?

Hello,

I have a nonlinear pde model which is mainly , and I do have the numerical solutions corresponding to some different time values, but I am not able to get its analytical solution.

I have been trying to use 'the lsqnonlin and lsqcurvefit functions' in Matlab to estimate one of my equation parameters. I have already defined the parameter \lambda and K where are in the above equation, and I would like to estimate the parameter D as setting the lsqcurvefit function. So I know that least square method work as below;

[name]=lsqcurvefit(handle,x0,xdata,ydata);

I have xdata (time points) and ydata (results corresponding to time points) and also x0, which is the initial value, but I could not able to set the function handle part because I do not have the analytical solution. I have a trouble at that point to develop the code.

I will be so glad indeed if someone can help me.

Regards,

Emine