I wanted to confirm my interpretation of the splitting approach for this problem.
My understanding is that at each timestep we first solve the recation equation based on the previous solution u_s to obtain an intermediate solution u* and then pass this to the diffusion equation to finally solve for current solution u_s+1 as shown below. Also, should we solve each subequation for the full or half the timestep (i.e. use dt vs. dt/2 in below equations)?
>> u* = u_s / (u_s + (1-u_s) * exp(-dt))
>> u^_s+1 = (u*)^ x exp(-k^2 * dt)
>> u_s+1 = F-1 (u^_s+1)
Thanks