Discontinuities when computing integration of error functions using integral function
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I am trying to integrate a function over a region in different time intervals. The integration looks something like this.
fun_uz = @(u)1./sqrt(u).*exp(-Z.^2./(2.*u));
fun_Y = @(u)(erf((Y+B)./sqrt(2.*u))-erf((Y-B)./sqrt(2.*u)));
fun_Z = @(u)(erf((X+L+u)./sqrt(2.*u))-erf((X-L+u)./sqrt(2.*u)));
fun = @(u)inc.*fun_uz(u).*fun_Y(u).*fun_Z(u);
fint = integral(fun,0,upperl);
The variable 'upperl' is the upper limit of the integral function. I have to perform this integration over different X,Y, and Z regions and different 'upperl' values. I am getting profiles which are discontinuous for different 'upperl' values. I have shown here profiles at few different 'upperl' values.
I am not able to understand why the discontinuity are occuring, any help is greatly appreciated. Thanks.
6 Comments
darova
on 19 Mar 2020
time = 1e-2; % The variable which is changed to generate different contour plots
xs = (-500:10:10)./1000;
Accepted Answer
darova
on 19 Mar 2020
The function you are trying to integrate looks like following
Put these lines inside for loops
ezplot(fun,[0 upperl])
pause(0.01)
When time > 0.1 upperl is big. When you call integral you don't know how many points it takes. Maybe it misses something
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More Answers (1)
Walter Roberson
on 20 Mar 2020
Change the integral to
fint = integral(fun,0,upperl, 'waypoints', L-X);
You have two erf that only have an input near 0 (and so a measurable output) near-ish -(X+L) to -(X-L) . Some of your integral() calls just happened to evaluate near there, and some of them did not happen to evaluate near there and predicted that there was nothing interesting in that area. The above forces evaluation near that area.
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