Evaluating a double integral using the trapezoidal rule

Question

Robert 2011-2-22

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1800-evaluating-a-double-integral-using-the-trapezoidal-rule

回答： Mohammed 2023-12-12

I am trying to take the double integral of the function using the Trapezoidal rule for G=integral (3*x.^2*y+cos(2*x)*sin(y)+2+4*y.^-2*x+5*y)dxdy with x interval 0 to 2pi and y interval 1 to 10. I found a formula for it but don't know the proper syntax to enter it in. We must use the trapezoidal rule because we are comparing different techniques for evaluating integrals. Here is what I have so far:

x1=0;
x2=2*pi;
y1=1;
y2=10;
N=101
dx=(x2-x1)/(N-1);
dy=(y2-y1)/(N-1);
x=x1:dx:x2;
y=y1:dy:y2;
g(x,y)=3*x.^2*y+cos(2*x)*sin(y)+2+4*y.^-2*x+5*y;
N=101;
for i=1:N+1
for j=1:N+1
    out(i,j)=((dx*dy)/4)*(g(i,j(1,1))+g(i,j(1,N))+g(i,j(N,1))+g(i,j(N,N))+2*(g(i,j(1,2:1:N-1))+g(i,j(N,2:1:N-1))+g(i,j(2:1:N-1,1))+g(i,j(2:1:N-1,N)))+4*(sum(g(i,j(2:1:N-1,2:1:N-1)))));
end
end

The really long formula is from this source: http://www.math.ohiou.edu/courses/math344/lecture24.pdf on page 2. I feel that I could streamline the code by using more summation but I do not know how to do that.

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Andrew Newell 2011-2-22

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1800-evaluating-a-double-integral-using-the-trapezoidal-rule#answer_2679

在 MATLAB Online 中打开

How about this:

N = 101;
x = linspace(0,2,N)*pi;
y = linspace(1,10,N);
dx = diff(x(1:2));
dy = diff(y(1:2));
[x,y] = meshgrid(x,y);
mat = 3*x.^2.*y+cos(2*x).*sin(y)+2+4*y.^(-2).*x+5.*y;
mat(2:end-1,:) = mat(2:end-1,:)*2;
mat(:,2:end-1) = mat(:,2:end-1)*2;
out = sum(mat(:))*dx*dy/4;