?c(r,t)/?t=L(c(r,t) )+D?^2 c(r,t)
how to discretize the time derivative?thanks
It really depends on what you are doing. For applied mathematics and engineering, discretizing the time dervivative may involve using finite differences, which it return make the equation as so
(C(r,t+1)-C(r,t))/(delta t)=L(c(r,t) + D*((c(r-1,t)-2*c(r,t)+c(r+1,t))/((delta r)^2)
This looks like some type of physical phenomena modeling, in this case finite differences (as dervived from taylor series expansion and dervivatives will do).... but to understand and calculate this.. you need to write a program in C++, Matlab, or your choice,as this requires iterations to solve. Numerical techniques like matrix inversion, A^-1*B=C will work, or Gauss Siedel Method to understand how to solve these differential equations. Look more into finite differences and applied mathematics to understand this and give me a shout out if you need more help.
http://www.public.asu.edu/~hhuang38/pde_note3.pdf
Best.
