need help please

My work is on implicit FDTD method which allows time step (delta_t) above CFL limit. Implicit methods require one to solve a large sparse matrix. If delta_t is increased the the solution of this sparse matrix becomes slower. I can see this when I do the simulation with the implicit scheme.

But my query is about mathematical explanation of what happens when I increase delta_t. How the properties of the matrix change with the change of delta_t which ultimately lead to poor convergence. Identifying this is very important as by this I can attempt to do something (like using appropriate pre-conditioners etc ) to accelerate the solution. Can you advise me which properties of the sparse matrix do I actually need to look into.

Also any advice on some easy literature / books where I can get a good understanding on this would be highly appreciated. If this is not a suitable
forum for this can you please refer me to some other more appropriate forum
where I can get advice on mathematical issues like this. Thank you very much.

for confi999
i think u should go for the book of D.M.sullivan for fdtd,in which you can get the mathematical explanation about time step and space step.
the sullivan book is avilable ,here

Added after 9 minutes:

here is the book by d.m.sullivan

Hi Smruti,
Although my query was about connection between dt and sparse matrix solution (probably related to perturbation theory of matrix), I do appreciate your advice on Sullivan's book. Thank you.