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Jan
18
comment Constructing the coefficient matrix in discretization of a PDE
By theoretical, I mean to have the entries of matrix $A$ in a symbolic way so as to find some region of stability based on the involved step sizes hx and hy along the two spatial directions. I believe that MMA could do that, however I am stuck in filling the matrix $A$ with the above piece of code! I obtained the general discretized formula as you may kindly see above, but I do not know how to deal with the doubled dimensions, i.e., $mn\times mn$. Maybe a reordering of the indices or a Kronecker product could produce the final coefficient matrix for some ordinary values $m=n=6$.
Jan
18
comment Constructing the coefficient matrix in discretization of a PDE
Thanks for the comments. They are very useful. Currently, $F$ is nonlinear and I just wish to apply the method of lines. That is why I am using the finite difference scheme. I know that NDSolve`FiniteDifferenceDerivative is really great, but it is hard to extract the matrices with theoretical entries from it. I mean, that is excellent for numerics. However, if you have some worked examples in 2D case, please put them here. Maybe, they could help more.
Jan
18
revised Constructing the coefficient matrix in discretization of a PDE
edited tags
Jan
18
comment Constructing the coefficient matrix in discretization of a PDE
I think the matrix $A$ is going to be a block tri-diagonal matrix.
Jan
18
asked Constructing the coefficient matrix in discretization of a PDE
Jan
14
comment How to speed up filling a matrix as much as possible in a loop?
Wow, your answer is unbelievable. It works perfectly and speed up the process of filling the matrix. Thanks a lot.
Jan
14
asked How to speed up filling a matrix as much as possible in a loop?
Jul
18
awarded  Notable Question
May
22
asked How to incorporate the boundary conditions into the differentiation scheme in MMA?
Apr
14
awarded  Yearling
Apr
14
awarded  Nice Question
Mar
31
awarded  Popular Question
Feb
1
awarded  Notable Question
Jul
2
awarded  Curious
Jun
12
asked How to find a scaling parameter in matrix inversion process by MMA?
Nov
20
awarded  Critic
Nov
19
comment Why doesn't FullSimplify work properly on this?
Note that $1+R+R^2+R^3+R^4+R^5+R^6$ requires 5 multiplications to be implemented, while $1+(R+R^4)(1+R+R^2)$ requires only 3! That is why a more factorized form is desirable.
Nov
19
asked Why doesn't FullSimplify work properly on this?
Oct
10
awarded  Popular Question
Sep
6
comment Faster Eigenvalues with lower precision goal
Can anyone extend this answer for the unsolved question at: mathematica.stackexchange.com/questions/29688/…