How to plot Error function of complex numbers

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HAREKRISHNA MANDAL
HAREKRISHNA MANDAL 2017-8-23
评论： Dilip Jose 2020-2-5
Dear sir how have plotted for complex function taking omega=pi/2, M=0.5

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John BG
John BG 2017-8-24
Hi Harekrishna Mandal
this is John BG <mailto:jgb2012@sky.com jgb2012@sky.com>
Although MATLAB standard functions erf and erfc only work with real inputs, there is the MATLAB implementation of erfc(z) z Complex, by S. Abrarov, available here
https://uk.mathworks.com/matlabcentral/fileexchange/47801-the-voigt-complex-error-function--second-version-?s_tid=srchtitle
fadf.m Attached to this answer for convenience.
I reach the following plots for a time interval of [0 10] dt=0.01 and sample theta=1
clear all;close all;clc;
M=.4;w=pi/2;
dt=0.01;t1=0;t2=10;t=[t1:dt:t2];
theta=1; % sample value
p7_1=.25*exp(-1j*w*t)*exp(theta*(M-1j*w)^.5).*fadf((M-1j*w).^.5+.5*theta./(t).^.5);
p7_2=.25*exp(-1j*w*t)*exp(-theta*(M-1j*w)^.5).*fadf(-(M-1j*w).^.5+.5*theta./(t).^.5);
p7_3=.25*exp(1j*w*t)*exp(theta*(M+1j*w)^.5).*fadf((M+1j*w).^.5+.5*theta./(t).^.5);
p7_4=.25*exp(1j*w*t)*exp(-theta*(M+1j*w)^.5).*fadf(-(M+1j*w).^.5+.5*theta./(t).^.5);
p7=p7_1+p7_2+p7_3+p7_4;
abs_p7=abs(p7);arg_p7=angle(p7);
re_p7=real(p7);im_p7=imag(p7);
figure(1);plot(t,abs_p7,t,arg_p7);grid on;legend('|p7|','ang(p7)');
figure(2);plot(t,re_p7,t,im_p7);grid on;legend('re(p7)','im(p7)');
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if you find this answer useful would you please be so kind to consider marking my answer as Accepted Answer?
To any other reader, if you find this answer useful please consider clicking on the thumbs-up vote link
thanks in advance
John BG
<mailto:jgb2012@sky.com jgb2012@sky.com>
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Dilip Jose
Dilip Jose 2020-2-5
sir ...for my problem symbolic variables exist in fadf....error..while compiling....
Example:-how plot this ...pls help me out
% velocity profile code
syms z
dt=0.01;t1=0;t2=5;t=(t1:dt:t2);
u=0.2;
s1=z;
w=0.5;
M=1;
m=((M+(2*1i*w))*u);
k=(fadf(z./(2*(t).^.5)+(M+(2*1i*w))*u).^.5);
re_k=real(k);im_k=imag(k);
plot(t,re_k,t,im_k)

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Walter Roberson
Walter Roberson 2017-8-24
The Symbolic Toolbox is happy to take erfc() of a complex number. After that it is just a matter of putting together the formulas, and deciding which representation one wishes to use for complex plots.
One plot method not mentioned in the link I posted first, is to draw in 3D, putting t on the x axis, real() of the expression on the y axis, and imag() of the expression on the z axis.

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