Reaction-Diffusion Equation with Highly Non-Linear Source Term

Hi, im currently trying to solve a 1D reaction-diffusion-equation system:

dc/dt = d/dx( -D dc/dx) + g*s(c,x)

It is somewhat similar to a heat equation or a Poisson equation. c is the vector of concentrations of some gases I want to know, D is a Diffusion coefficient (~1E-5) and g a geometrical factor (~1E+5).

The difficulty lies in the highly non-linear behavior due to the source term combined with the geometrical factor. The source term is a function of the solution c itself. I tried to discretize my domain with Finite Differences and then use ODE15S to solve the equation in time, but this approach is realy unstable for my conditions.

Is there any other approach I could use?

Thank you for any suggestions!