by Cuchulainn » Mon Aug 27, 2007 8:43 am
I would be interested in your opinion on the following special matrix A and then calculate exp(-At) (no integral for the moment). I have not coded it and do not have MM. It's probably very easy in MM.
The matrix A is (for moment) constant coefficient(ed). In particular it is tridiagonal and Toeplitz, meaning that it has 3 diagonals and each diagonal (sub, mid, low) has constant value.
SUB: the value is a - b where a and b are arbitrary real numbers
MID: value is -2a
LOW: value is a + b
Note A is not symmetric and may have complex eigenvalues.
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background
If you semi-discretise
U_t = aU_xx + BU_x
using centred FD in x you get an ODE
V_t = AV
with solution V(t) = V(0) exp(A)
Most times we use Crank Nicolson which is just a Pade(1,1) O(dt^2) approximation.
Any ideas?