<p>Numerical Inverse Laplace Transform</p>

63e1c1d4-3b8f-4f6a-bb18-4299a6f7b7b3 4 3 12 decimal

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Based on algorithm of Oscar: https://en.smath.info/forum/yaf_postst1341_Signals-and-Systems.aspx

1 F t.i t.e N a ns nd ILap t N 1 matrix : ft t : 12 mat U t.e t.i - UnitsOf : m ns nd + 1 + : 12 mat t.o 105 -^U * t.i 12 mat max eval : Δt t.e t.o - N 1 - / : 12 mat α m 1 matrix : β α : γ nd 1 matrix : 13 mat n 1 m range : α n el a n 1 - (π * i * + eval : β n el 1 - (n 1 +^: 13 mat n h nd 1 + Γ 2 nd^nd 2 + n - Γ * n Γ * / eval : n 2 nd range : γ 1 el 1 h : γ n el n h γ n 1 - el + : 13 mat n ns 3 + (m range : β 1 el 0.5 β 1 el * : β n el β n el γ m n - 1 + el * : 13 mat α α : β e a^β * eval : 12 mat k 1 N range t k el t.o k 1 - (Δt * + : st α t k el / : βt β t k el / : 13 mat ft k el βt st F * Re vectorize eval sum : 21 line for t ft augment eval 111 line :

1 FF t t.i t.e N ILap FT s# FF t.i t.e N ILap 1 el ILap 2 el ILap 3 el ILap : U FT 11 el UnitsOf FT 12 el UnitsOf 12 mat : U 2 el FT 1 col U 1 el / FT 2 col U 2 el / t U 1 el / cinterp * t.i t ≤ (* t t.e ≤ (* 31 line :

ILap 6201913 mat :

a ns nd 13 mat

Γ.κ 0.99999999999999709182 57.156235665862923517 59.597960355475491248 - 14.136097974741747174 0.49191381609762019978 - 0.33994649984811888699 104 -^* 0.46523628927048575665 104 -^* 0.98374475304879564677 104 -^* - 0.15808870322491248884 103 -^* 0.21026444172410488319 103 -^* - 0.21743961811521264320 103 -^* 0.16431810653676389022 103 -^* - 0.84418223983852743293 104 -^* 0.26190838401581408670 104 -^* - 0.36899182659531622704 105 -^* 151 mat :

ζ Γ z ζ 1 - : zh 1 - 2 ζ * + 2 / : zg zh 607128 / + : 13 mat 2 π * sqrt zg 0.5 zh *^(2^* e zg^/ Γ.κ 1 el Γ.κ κ 1 + el z κ + / κ 114 sum + (* eval 21 line :

Valid for Re(ζ)>0

Heaviside x Φ 1 x sign + 2 / :

a b c d s f a s * b s 2^* c s * + d + / :

a b c d t C a b c d s f s t invlaplace maple :

a b c d t C a c t * 2 b * / - exp * 4 d * b * c 2^- b 2^/ sqrt t * 2 / cos 4 d * b * c 2^- (* 4 d * b * c 2^- b 2^/ sqrt c * 4 d * b * c 2^- b 2^/ sqrt t * 2 / sin * b * - (* 4 d * b * c 2^- (b * /

a 0.5 : b 0.001 : c 0.33 : d 4.75 : 41 mat

x c 10 x ≤ (x 0.1 ≤ (& cases :

x L a b c d x C Re x c * :

x L 2 1 sys