I have the following PDE
My Question: I have done manually following calculations. I want to verify the following operations are right, or not by MAPLE. Could you help me, please?
In here, is an Nx1 matrix, P, C are NxN matrices. (N is an integer and superscript T denotes the transpose of the matrix.) and P are given matrices. But the matrix C is ungiven I will find it in the final step. But my question doesn' t include all steps. I just wonder how to calculate the first two steps by Maple.
( If Maple doesn' t do matrix algebra, we can treat them as if , P, C were not matrix. I think the result won' t be changed. We will get again equation 9 by Maple.)
We will find the followings
in terms of the matrices , P and C.
So, if we integrate Equation (2) with respect to x (from 0 to x), and by using the following two assumptions
substituting x=1 in Equation (3)
if rewrite Eqn. (4), we have
substituting Eqn. (5) to Eqn. (3), we have
integrating Equation (3) with respect to t,
If we integrate Equation (2) from 0 to x with respect to t, we have
Second Step We will substitute the terms to the pde ( Equation 1)
Substituting Eqn. (6), (7), (8) to Eqn. (1), we have finally
I want to do the above calculations by Maple.
Because I have more complex questions than above, I want to write a Maple code in order to avoid calculation errors.
Final Step for curious: it's hard to explain the whole method here. Briefly, we will discretize equation 9 for some collocation points t and x. And after doing it, we will have a system of an algebraic equation. (N equation and N unknown ( C is Nx1 unknown vector to be find) )
And then we will substitute vector C to Eqn. 7
Code for Matrices , P^1, P^2,etc.