Integrate PDEPE solution wrt x

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Jayant Choudhary 2020-6-17

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评论： Jayant Choudhary 2020-6-19

采纳的回答： Bjorn Gustavsson

I have solved a 1D spherical Diffusion PDE using pdepe in Matlab, which has given me Concentration(x,t) {=

} as a 2D array Now in continuation of my research, I need to find Stress as a function of distance and time {=

}, whose expression has terms of

and

. How should I tackle this part, ie, integrate x^2.C(x,t) wrt x.

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Answer 1

Bjorn Gustavsson 2020-6-17

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This rather straightforward method should get the job done (assuming you cannot get away with simply use trapz, or cumtrapz, but will definitely need the integral at "all" points in x and y and not only the ones you got out of the PDE-solution of C):

C = peaks(123); % Just making up some mock-up data
x = 0:122;      % and X
t = 0:122;      % and t-coordinates
[X,T] = meshgrid(x,t);
I1 = @(t,a,b) integral(@(x) interp2(X,T,P,x,t),a,b)
% this gives you a function to evaluate for any time and point along x, 
% below for time 12 s integration boundaries from 3 to 37
I1(12,3,37)

HTH

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Bjorn Gustavsson 2020-6-19

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Ok, if you're a recent matlaber, then I guess the anonymous functions are one of the most tricky parts to wrap your head around. Take some time to really grasp that construct.

In this case you don't integrate a matrix, in my solution you integrate a function where the function calculates the function-values by interpolation of the C matrix for an arbitrary point in time and along all values of x that the integral-function asks for. That way you should be able to modify the function I used to something like:

@(x) x.^2.*interp2(X,T,P,x,t)

Instead of what I used.

Jayant Choudhary 2020-6-19