I don't understand what you are asking. I assume that you have a model of a PDE solution, and that your model has a few parameters. nlinfit requires only that your modelfun argument be "...a function handle. modelfun must accept two input arguments, a coefficient vector and an array X—in that order—and return a vector of fitted response values." There is nothing in that description that requires an analytic expression for your nonlinear model function.
Alan Weiss
MATLAB mathematical toolbox documentation
