how to evaluate a double integral using the trapezoidal rule equation?

Question

Susan Santiago 2018-4-15

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https://ww2.mathworks.cn/matlabcentral/answers/395030-how-to-evaluate-a-double-integral-using-the-trapezoidal-rule-equation

回答： Apoorv Rajput 2021-10-7

Here's what I have so far

function [ I ] = myTrapz2D( f, x0, xn, y0, yn, nx, ny ) 
dx = (xn - x0)/nx;
dy = (yn - y0)/ny;
i = 1;
sumx = zeros(nx,1);
sumy =zeros(ny,1);
 while i < nx
    xi = x0 + i*dx;
    sumx(i) = f(xi);
    i = i+1;
end
sumx = sum(sumx);
Ix = ((dx)/2)*(f(x0)+f(xn)+(2*sumx));
fd = Ix(y);
 while i < ny
    yi = y0 + i*dy;
    sumy(i) = fd(yi);
    i = i+1;
end
sumy = sum(sumy);
 I =((dy)/2)*(fd(y0)+fd(yn)+(2*sumy));
  end

not sure if it's correct at all but it has to be solved using some variation of the equation for I that I used. I keep getting an error that there aren't enough input arguments. There are my input arguments: f = @(x,y) x.^2 - (2*y.^2) + (x.*y.^3); x0 = 0; xn = 2; y0 = -1; yn = 1; nx = 8; ny = 8;

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Answer 1

Torsten 2018-4-16

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https://ww2.mathworks.cn/matlabcentral/answers/395030-how-to-evaluate-a-double-integral-using-the-trapezoidal-rule-equation#answer_315330

You don't need to program the trapezoidal rule in two dimensions.

Just call the trapezoidal rule in one dimension twice. In the section "Multiple Numeical Integrations" under

https://de.mathworks.com/help/matlab/ref/trapz.html

is an example with the MATALB implementation of the trapezoidal rule "trapz".

Best wishes

Torsten.

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Susan Santiago 2018-4-17

yes, I'm away that this can be done using trapz, however my assignment involved creating a function like the one I have shown you so, in this case, trapz does not help

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Answer 2

Apoorv Rajput 2021-10-7

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/395030-how-to-evaluate-a-double-integral-using-the-trapezoidal-rule-equation#answer_803256

在 MATLAB Online 中打开

function [ I ] = myTrapz2D( x0, xn, y0, yn, nx, ny ) 
syms f(x,y);
syms x;
syms y;
f(x,y)=exp(y-x);
dx = (xn - x0)/nx;
dy = (yn - y0)/ny;
i = 1;
sumx=0*x*y;
 while i < nx
    xi = x0 + i*dx;
    sumx=sumx+ f(xi,y);
    i = i+1;
 end
Ix = ((dx)/2)*(f(x0,y)+f(xn,y)+(2*sumx));
syms fd(y);
fd(y) = Ix;
sumy=0*y;
i=1;
 while i < ny
    yi = y0 + i*dy;
    sumy= sumy+fd(yi);
    i = i+1;
 end
 I =((dy)/2)*(fd(y0)+fd(yn)+(2*sumy));
  end