I tried to make numerical integration of function for continuous (7.nb) and discrete times (9.nb). I have the following questions concerning discrete time:
1. with logarithmic scale values of time more than 4?? are not shown, but I need to get less than 1???.
2. with linear scale, on the contrary there appears ???????? 2us, although in the original array the maximum value is 1us
3. while calculating coefficient (at the bottom of file) the program says about dixision by 0. But it is not possible, as in Mathcad I get the result of about 10^-12
4. function z is not calculated, but it exists analytically
http://zalil.ru/34911397/5efb62f5.52dc96a8/9.nb9.nb
c = 3*10^8;H = 7.2*10^5;\ = 47*10^-6;Fd = 7200;Tp = 50*10^-6;f = 3.5*10^8;v = 7500;Q = 18000;L = 100;s2 = 0.003;s1 = 2;\0 = 0.018;m = 256;\ = 0.022;n = 3;lm = 25;d = 1.2;\ = 0.022;n = 3;P0 = 25;\ = 0.8;KIP = 0.4;kf = Sqrt[0.5];\s = 1;t = Sort@{-10^-8, -20^-9, -10^-9, 0, 10^-11, 10^-10, 10^-9, 10^-8, 20*10^-7, 2*10^-6, 10^-6};p = Sum[NIntegrate[ Exp[(\ Fd^2 Tp^2 (m - Abs)^2 x^2)/ H^2 - (n^2 \^2 d^2 y^2)/(\0^2 \^2 \H^2*141^2) - (100 lm^2 x^2 s1^2)/(H^2 L^2 \^2 s2^2) - (100 lm^2 \y^2*s1^2)/(H^2 L^2 \^2 s2^2) - (5.55 (y^2 + x^2))/(H^2 \0^2) - \ (f^2 (t - k Tp - x^2/(c H) - y^2/(c H))^2 + 2 Q (v k Tp)/(H d) + \^2 ((v k Tp)/(H d))^2)], {x, \-Infinity, Infinity}, {y, -Infinity, Infinity}, MaxRecursion -> 40, AccuracyGoal -> 60, Method -> "AdaptiveMonteCarlo"], {k, -255, 255}];ListLogPlot[Transpose[{t, p}], Joined -> True, PlotRange -> All]
ListPlot[Transpose[{t, p}], Joined -> True, PlotRange -> All](P0*((4*\ (\* d^2)/^4)/\^2)^2*\^2*f*\*KIP*\*kf^2)/(64*\\^2*H^2)Exp[-((16*\^2*s2^2)/\^2)](d^4 f kf^2 KIP P0 \^2 \ \)/(4 H^2 Null^8 \^2)E^(-((16 \^2 s2^2)/\^2))(P0*((4*\ (\* d^2)/^4)/\^2)^2*\^2*f*\*KIP*\*kf^2*c)/(\32*\^2*H^3*s1^2)(c d^4 f kf^2 KIP P0 \^2 \ \)/(2 H^3 Null^8 s1^2 \\^2)z = Sum[NIntegrate[ Exp[-(5.55* r^2)/(H^2 *\0^2) - (11.1* r*\s^2*Cos[\])/(H *\0^2) - r^2/(H^2 *s1^2) - \* f^2*(t - k Tp - r^2/(c H) - \)^2], {\, -Infinity, Infinity}, {r, 0, Infinity}, {\, 0, 2*\}, MaxRecursion -> 40, AccuracyGoal -> 60, Method -> "AdaptiveMonteCarlo"], {k, -255, 255}];ListPlot[Transpose[{t, z}], Joined -> True, PlotRange -> All]
Questions concerning continuous time:
1. Why doesn't the graph show anything?
http://zalil.ru/34911400/5efb62f5.52dc96a8/7.nb7.nb
c = 3*10^8;
H = 7.2*10^5;
\ = 47*10^-6;
Fd = 7200;
Tp = 50*10^-6;
f = 3.5*10^8;
v = 7500;
Q = 18000;
L = 100;
s2 = 0.003;
s1 = 2;
\0 = 0.018;
m = 256;
\ = 0.022;
n = 3;
lm = 25;
d = 1.2;
\ = 0.022;
n = 3;
p := Sum[
NIntegrate[
Exp[(\*Fd^2*Tp^2*(m - Abs)^2*x^2)/
H^2 - (n^2*\^2*d^2*y^2)/(\0^2*\^2*
H^2*141^2) - (100*lm^2*x^2*s1^2)/(H^2*L^2*\^2*
s2^2) - (100*lm^2*y^2*s1^2)/(H^2*L^2*\^2*
s2^2) - (5.55*(y^2 +
x^2))/(H^2*\0^2) - \*(f^2*(tt - k*Tp -
x^2/(c*H) - y^2/(c*H))^2 +
2*Q*(v*k*Tp)/(H*
d) + \^2*((v*k*Tp)/(H*d))^2)], {x, -Infinity,
Infinity}, {y, -Infinity, Infinity}, MaxRecursion -> 40,
AccuracyGoal -> 60, Method -> "AdaptiveMonteCarlo"], {k, -255,
255}];
Plot[p[t_], {t, -10^(-8), 10^(-6)}, PlotPoints -> 30,
MaxRecursion -> 0]
I would like to correct it with your help.