cf071494-082a-4f0e-a4bc-260c77b68c9d 28 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Mesh  within the bounds L, H L H N xd N intervals U 0 : dx H L - N / : i 1 N range U i el L dx i * dx - (+ : for U 51 line :

Solving for a vector of values

x f x 2 π * / 2 π * x / tanh * sqrt :

In Mathematics, an InverseFunction is the solution of this function. f(x) is the model of difficulty documented in Mathematica 4.0. The seeded solve scanner is of no gain versus the direct "Sol". The 'roots' can't be applied wrt the derivative that does not take discrete vector of values. In lieu, the 'solve' block concludes pretty well.. a bit slow. The seeded scanner is interesting in the sense that it can be invoked as a function.

0.06 0.99 0.07 range 0.02 2012 mat 12 mat

t0 1 time :

Sol 93 sampled values, 22 sec ω 0.06 0.99 0.07 range : j 1 ω rows range sol j el η f ω j el - 0 ≡ η 0.02 20 solve : for ω sol augment 41 line :

Note: the function starts existing around 'x = 0.02, f(0.02) = 0.0564' our choice to solve is wise , down to lower possible limit. The upper limit 0.99 is practical. In fact, at 1, the solution is infinite. Pushing a bit more 'solve' cries to murder.

Sol

1 time t0 - 22 sec *

t0 1 time :

ω 0.06 0.99 100 xd :

ω η inv η f ω - 0 ≡ η 0.02 20 solve :

n η sol 100 samples n:90 27 sec i 1 n range t i el ω i el η inv : for η t n el : i n ω rows range seeded after n η ω i 1 - el η inv : t i el ω i el η inv : 31 line for ω t augment 51 line :

90 η sol

1 time t0 - 27 sec *