Diffusion with reversible Binding

I am trying to model one dimensional diffusion with reversible binding. Essentially my situation is A+B - AB where thre is a Kon , Koff, and a Kd. Where I know the concentration of "B" 9they lie along a line, and I let A diffuse around and bind. I would like to plot the concentration profiles along the line after different amounts of time. I have solved this problem for when [A] << Kd of the reaction, in that case there is an analytical solution and all is well. I am now trying to solve the general case (i.e. [A] can be >= Kd of the reaction). i believe i've got the problem down to the following sets of equations :

1) Cxx -Ct = E/F*Nt

2) ENt = GF*C(1-N)-GN

whereC is the concentration of species A Cxx and Ct are the double-space and time derivatived of the concentration and Nt is the time derivative of the number of occupied sites of, and N is the number of occupied sites. the rest (EFG) are just constants. I believe these are coupled, secondorder nonlinear PODE's. Can someone point me to where to look to help me solve them... thanks...