MATLAB: Double integral with singularity

integration with singularity

Hi, I want to integrate the following equation (singularity at t = \tau)
1./sqrt(4*pi*(t-\tau)).*exp(-(x - \xi).^2./(4*(t-\tau)));
space x = (-10 <= x <= 10), time t = (0 <= t <= 2.1)
variable of integration \xi, \tau
\xi = x,  0 < \tau < t
So I tried as following code.
x = linspace(-10, 10, 41);
t = linspace(0.1, 2.1, 41);
xi = x;
ta = t;
nx = length(x);  % number of interval of x
nt = length(t);  % number of interval of t
for mt = 1:nt
    for mx = 1:nx
        GLA = @(ta, xi) 1./sqrt(4*pi*(t(mt)-ta)).*exp(-(x(mx) - xi).^2 ...
            ./(4*(t(mt)-ta)));
        funGLA = quad2d(GLA, 0.05, ta(mt), xi(1), xi(end));
        Int_GLA(mt, mx) = funGA;
    end
end
However, it leads to wrong results. I don't know what's wrong. Could you help me?

Best Answer

I will change my earlier comment into an answer:
Look at these two lines:
 funGLA = quad2d(GLA, 0.05, ta(mt), xi(1), xi(end));
 Int_GLA(mt, mx) = funGA;
You are calculating funGLA but then you are saying Int_GLA(mt,mx) = funGA
funGA is a variable remaining from an earlier calculation, and so every value of Int_GLA is getting assigned to that same number. You should first correct that mistake, and then see if that helps anything.
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