Question: Finding optimal values of some parameters

I wrote a code.mw for a numerical method for a PDE. (You can find the numerical method, exact solution and error between them in the code.)

The method depends on parameters k, M, which are any positive integers, and also depends on teta, beta>-1 which are real numbers.

According to the used method,

when k and M increase, we expect that the error (exact-numeric) generally decreases. 

In the code, I selected k=2, M=2, teta=1 and beta=1. And so k=2, M=2, CPU time is low. Error is not bad.

But for k=4, M=3 and also for bigger values of them, CPU time is high. I can' t get the solution.

Question 1: 

I don't know, but it may be possible to simplify the code in order to calculate for k=4, M=4?

Question 2:

I want to find optimal values of teta and beta for minimizing the error between numerical and exact solution, when k=2, M=2, or k=3, M=1 etc.

How can we write a Maple code for finding optimal values of teta and beta?

You can download the code.mw