need halp with simbolic summation?

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d 2016-12-6

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评论： Karan Gill 2016-12-8

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I solved the laplace equation and I got a discrete vector of coefficients (A_n) with 100 coefs (n=100)

now the solution is looking like this:

U(i,j)=sum(An.*cosh((pi/b*(1/2+n))*z(j)).*sin((pi/b*(1/2+n))*(x(i)-b)));

where x,z are the coordinates and n is the index

now I need to plot it. the straight forward method would be to calculate the sum in each coordinate, using two for loops

 for i=1:length(x)
    for j=1:length(z)
        U(i,j)=sum(An.*cosh(Ln*z(j)).*sin(Ln*(x(i)-b)));
    end
 end

I dont want to use repmat tools because x,z can get very large and I also want to check for larger n (n=1000, n=10000) so it will consume too much memory.

Is there a different way to do it? I thought maybe to use symbolic? but I dont know how to use symbolic symsum when A_n is a vector and not an expression.

I tried this:

 syms x z b
 b=0.3;
 U=symsum(An(n).*cosh((pi/b*(1/2+n))*z).*sin((pi/b*(1/2+n))*(x-b)), i, 1,  10);

but it didn't work. any suggestions?

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Karan Gill 2016-12-8

You already have numeric data. Why are you going to symbolic? You are supposed to go the other way. I'd recommend finding a way to optimize your numeric calculations.

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