Composite Trapezoid rule

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Jason 2011-4-9

1
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/5142-composite-trapezoid-rule

回答： Sulaymon Eshkabilov 2020-9-11

I know for a single integral you would use the cumtrapz function. I have a problem where I have to use the composite trapz rule on a double integral and I can find nothing on how to do that. The function is

(x^2 - 2y^2 +xy^3)dxdy where the outer y limits are -1:1 the inner x limits are 0:2 and n = 2

Any help would be much appreciated. The answer is supposed to be 2.

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Jason 2011-4-11

Jiro, I really appreciate that. I finally found somewhat similar application of the com trapz rule that I was able to use to figure it out. I was close originally and it was just missing a simple step. I have never used meshgrid, nor has it been discussed in class to this point so I would never have thought of using it nor would I know how to. Thank you for taking a moment to explain it. I already have the problem figured out but the meshgrid information will be useful in the future.

Jason 2011-4-11

To clarify the missing part of what I had was to divide the entire B expression by 2n, which in this case would be 4. It's just too obvious, but looking at the basic form of the composite trapezoidal rule clearly shows it. Thanks again for the help even though it was something simple I missed.

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回答（1 个）

Sulaymon Eshkabilov 2020-9-11

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/5142-composite-trapezoid-rule#answer_493306

Here is a simple solution to this exercise:

x = -1:0.02:1;
y = -1:0.025:1;
[xx,yy] = meshgrid(x,y);
Fun = xx.^2 -2*yy.^2+xx.*yy.^2;
ALL = cumtrapz(y,cumtrapz(x,Fun,2));
mesh(xx,yy,Fun)
xlabel('x')
ylabel('y')
str = '$$ \int_{-1}^{1} \int_{-1}^{1} (x^2 -2*y^2+x*y^2 )dxdy $$';
zlabel(str,'Interpreter','latex')
hold on
surf(xx,yy,ALL,'FaceAlpha',0.5,'EdgeColor','none')
plot3(xx(end),yy(end),ALL(end),'md', 'markerfacecolor', 'c')
v = [1 1 1];
view(v);