Discontinuities when computing integration of error functions using integral function

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Yaswanth Sai 2020-3-19

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编辑： Yaswanth Sai 2020-3-20

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.

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darova 2020-3-19

在 MATLAB Online 中打开

time = 1e-2; % The variable which is changed to generate different contour plots
xs = (-500:10:10)./1000;

Yaswanth Sai 2020-3-19

Yeah, the code works for smaller time values of order 10^(-2) and lesser, but is not working for values greater than that of order 10^(-1) and higher.

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darova 2020-3-19

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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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Walter Roberson 2020-3-20

I do not see the whole code posted ?

Yaswanth Sai 2020-3-20

I added the edited code

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Walter Roberson 2020-3-20

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https://ww2.mathworks.cn/matlabcentral/answers/511691-discontinuities-when-computing-integration-of-error-functions-using-integral-function#answer_421026

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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.