The name is absent

matrix A. Discretizing this form in time as well yields:

‰ι = ⅛ + ɪ(z - ɪʌfi - ɪɪf')df
C√ Jλ,_c ιt_m

where I is the identity matrix. This integration scheme is called ’’forward euler”, and is
stable as long as 2dt < τ. It is an explicit scheme that relies on the slope of the voltage at
the current time point t to predict the future voltage at t + 1. A scheme which gives better
stability is:

di + ⅛-ι)               (5.13)

This scheme is called ’’backwards euler,” and an ’’implicit” scheme in that a system of
equations must be solved to find the voltage at time t from time t - 1.

This scheme can be expanded to model a two-dimensional network by changing A from
the tridiagonal second difference form to the difference matrix for the two dimensional
laplacian operator v². This matrix can be computed by taking the sum of the Kronecker
tensor products of the identity matrix and one-dimensional second difference matrix plus
the tensor product of the one-dimensional second difference matrix with the identity matrix
[81].

Finally, the steady-state distribution can be solved by eliminating the capacitance from
this model, where A can represent the Id or 2d difference matrix:

1        1 ∖ ʌ     ^

— I^ι    AI v_ss — i                              (5.14)

ʃɪm    ʃɛe /

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