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Double Integral for Discrete Function

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Raees
Raees 2016-8-17
评论： Raees 2016-8-19
Dear All, I am solving a PDE in which I have to find the double integral of a discreet function. PDE has the following form:
where F(x,y) is a matrix of size (M,N), obtained by solving another PDE.
[F,x,y]=some_funtion_to_solve_PDE(some inputs);
I'll use some initial guess for G(x,y) within the integral which also gives me a matrix of the same size as F(x,y).
Here the integrand is a product of two discrete functions and the integral limits are numbers. Matlab built-in routine quad2d() requires the integrand to be a continuous function of x & y. Similarly, the other routines like integral2() also require continuous function expressions. I need help and suggestions on solving this double integral with discrete function, which will enable me to solve the PDE. Many Thanks.

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Torsten
Torsten 2016-8-17
Take a look at the example "Multiple Numerical Integrations" under
http://de.mathworks.com/help/matlab/ref/trapz.html
Best wishes
Torsten.
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Torsten
Torsten 2016-8-18
编辑：Torsten 2016-8-18
I just chose an analytical function form to create the matrix F for the sake of convenience.
F can be any matrix you like, as long as F has dimension
(length(y)) x (length(x))
Best wishes
Torsten.
Raees
Raees 2016-8-19
Thanks, Torsten. This time, it worked. So nice of you.

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