<p> Numerical Inverse Laplace Transform ... [a,ns,nd] </p>

2dc93b07-59d6-4ad5-895b-fb975c399227 16 3 12 decimal

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

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

Algo style adapted from Oscar

s F t invLaplace t 1 el 106 -^: 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 :

s F 1 s 2^L C * (* s R C * (* + 1 + / :

s F s t invlaplace maple

ε 1012 -^:

user range/mesh t.ini ε : t.end 5 : pts 100 : 13 mat

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

x c 10 x ≤ cases :

R 0.5 : L 1 : C 0.5 : 13 mat

RLC s F t invLaplace :

R L C t f 2 R t * 2 L * / - exp * L * 4 L * - R 2^C * + L 2^C * / - sqrt * 4 L * - R 2^C * + L 2^C * / - sqrt t * 2 / sin * 4 L * - R 2^C * + / - :

RLC R L C x f x c * 2 1 sys

http://www.phys.ufl.edu/courses/phy2054/s09/lectures/2054_ch21A.pdf

1. By series/parallel rules 2. L, C have 0 initial conditions

s L 12 s * C * / 4 s * L * 1 R * 4 s * L * + / + 3 R * + (:

Copy/paste in blank work sheet ... proceed s L t 0 > assume s t invlaplace maple

x c 10 x ≤ cases :

R 1 : L 0.25 : C 1 : 13 mat

t XFR 2 L * R R t * 4 L * / - exp * C * - 4 L * C * / :

x XFR x c * x abs XFR 2 1 sys

x XFR x c * x abs XFR 21 sys

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 * / ≡