Δinc(f(▄),L,Δ,N)

6d169e5f-bc29-4358-8691-2fce7e510feb 7 3 12 decimal

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

Δinc(f(▄),L,Δ,N)

# f L Δ N Δinc X 0 : i 1 N range X i 1 + el L Δ i * + : X 1 el L : 21 line for i 1 X rows range vy i el X i el f : for X vy augment 41 line :

in program ... user a 6 : ns 10 : nd 9 : 13 mat

Numerical Inverse Laplace Transform ... [a,ns,nd]

s F t invLaplace t 1 el 105 -^: t.ini 0 ≡ t cases [a,ns,nd] user comman line n 1 ns nd + 1 + (range α n el a n 1 - (π * i * + : β n el e a^1 - (n^* - : 21 line for bdif 1 el nd 1 + Gamma nd 2 + 1 - Gamma / 1 Gamma / (: β2 β ns 2 + (ns 1 + nd + (range 11 range el : n 2 nd range bdif n el nd 1 + Gamma nd 2 + n - Gamma / n Gamma / (bdif n 1 - el + : for bdif bdif reverse 2 nd^/ : n 1 nd range β2 n el β2 n el bdif n el * : for β β 1 ns 1 + (range 11 range el β2 stack : β 1 el β 1 el 2 / : 41 line kt 1 pts range tt t kt el : s α tt / : βt β tt / : n 1 α length range βtF n el βt n el s n el F * : for RβtF βtF Re : ft kt el RβtF eval sum : 61 line for OUT t ft augment : 91 line :

Reluctant companions ! ... partwise

ttt q2 ttt - exp - : σ L2 ttt q2 ttt σ laplace maple : 21 sys

ttt q1 1 : σ L1 ttt q1 ttt σ laplace maple : 21 sys

s λaplace s L1 s L2 + : 11 s + (s * /

1 s / 11 s + / - 11 s + (s * / ≡

s F 11 s + (s * / :

t Φ s F t 0 > assume s t invlaplace maple :

user range/mesh t.ini 0 : t.end 3 : pts 100 : 13 mat

in-situ incremental t t.ini t.end t.end t.ini - (pts 1 - / range :

x Ω x Φ : L 1 : Δ 0.1 : N 50 : 13 mat maple x Ω L Δ N Δinc : 31 sys

x c 10 x ≤ cases :

Export s F t invLaplace :

User XFR parameters [H, γ, T]

Export x Φ x c * 2 1 sys maple x Φ x c * 2 1 sys

Export 00 0.03 0.03 0.061 0.059 0.091 0.087 0.121 0.114 0.152 0.141 0.182 0.166 0.212 0.191 0.242 0.215 0.273 0.239 0.303 0.261 0.333 0.283 122 mat

maple 1 0.632 1.1 0.667 1.2 0.699 1.3 0.727 1.4 0.753 1.5 0.777 1.6 0.798 1.7 0.817 1.8 0.835 1.9 0.85 2 0.865 2.1 0.878 122 mat

Notes . . .

numerical Laplace or maple is a matter of project.

The maple is essentially an incremental algo.

The exported data set is equally spaced.

Same technique may be applied to numerical.

Incremental enables user to range the export at will

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