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I am trying to integrate product of two Green's functions and plot the results using Maxima. The problem is that Green's functions have singularities.

$ I=\int_{-\infty}^{+\infty}dxG1(x)G2(x)(F1(x)-F2(x))$

and

$ G1(x) = \frac{1}{ (x-0.1)+0.5+0.00001i} $

$ G2(x) = \frac{1}{ (x-0.1)+0.5-0.00001i} $

$ F1(x) = \frac{1}{ 1+e^{\frac{x}{0.2}}}$

$ F2(x) = \frac{1}{ 1+e^{\frac{x+0.4}{0.2}}}$

When I use wxMaxima (CAS), it fails to integrate and it fails to plot the solution y. I know that the solution plot should look like a smoothed step function where rising edge should be at x=0.1.

Any suggestions how to code wxMaxima/mathematica is appreciated. Thanks.

Aschoolar
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  • Your question looks unclear to me, or maybe I am missing something, starting with: I don't know what/which Green's functions you have. Then, is x real? If so integrating over x results in a numerical solution (numerically: ~1.2x10^5) but not a y(x) plot. Also, for x real, G1G2(F1-F2) has no singularities (only a sharp peak at x=-0.4). Also not clear what (CAS) is, though probably not relevant. – Rolazaro Azeveires Feb 11 '18 at 04:07

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