How to plot Error function of complex numbers

Dear sir how have plotted for complex function taking omega=pi/2, M=0.5

[Walter Roberson]

https://www.mathworks.com/help/matlab/creating_plots/plot-imaginary-and-complex-data.html

Answer 1

[John BG]

Hi Harekrishna Mandal

this is John BG <mailto:[e-mail] [e-mail]>

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:[e-mail] [e-mail]>

[HAREKRISHNA MANDAL]

What about fadf; error "Undefined function 'fadf' for input arguments of type 'double'."

[Walter Roberson]

Install the file exchange contribution that John linked to.

[John BG]

HARAKRISHNA

Use the fadf.m I have attached to my answer. Click on fadf.m right next to the header of my answer, to download it from my answer.

Or download it from

https://uk.mathworks.com/matlabcentral/fileexchange/47801-the-voigt-complex-error-function--second-version-?s_tid=srchtitle

Walter, thanks for the comment.

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:[e-mail] [e-mail]>

[Dilip Jose]

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)

[Dilip Jose]

sir pls reply

Answer 2

[Walter Roberson]

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.