How to plot results from Simpson's Rule integration?

Question

JoBrr 2020-10-15

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/614263-how-to-plot-results-from-simpson-s-rule-integration

评论： JoBrr 2020-10-15

Hi All,

I am currently trying to do some integration using the Simpson's rule. My codes does produce the required approximation. But I don't understand how I can obtain a plot of the number of panels (x-axis) vs the integral evaluated at each panel (y-axis). My code uses 10 panels. The plot should be some what of a zig zag in appearance. Could someone please provide some assistance regarding this matter?

My code is shown below:

%Function to be integrated
f=@(x)exp(x); 
%lower limit
a=0;
%upper limit
b=1; 
%number of panels
n=10; 
%interval size
h=(b-a)/n;
%summation of first two values
s=f(a)+f(b);
%loop for the rest of the calculations
for i=1:2:n-1
    s=s+4*f(a+i*h); %summation
end
for i=2:2:n-2
    s=s+2*f(a+i*h); %summation
end
%evaluate integral
I=h/3*s

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Answer 1

Asad (Mehrzad) Khoddam 2020-10-15

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/614263-how-to-plot-results-from-simpson-s-rule-integration#answer_514228

在 MATLAB Online 中打开

function ask005
%Function to be integrated
f=@(x)exp(x); 
%lower limit
a=0;
%upper limit
b=1; 
N=[10, 20, 40, 100, 200, 400, 800, 1000];
In = NaN(size(N));
%number of panels
for j = 1:length(N)
    %interval size
    n=N(j);
    h=(b-a)/n;
    
    %summation of first two values
    s=f(a)+f(b);
    
    %loop for the rest of the calculations
    for i=1:2:n-1
        s=s+4*f(a+i*h); %summation
    end
    
    for i=2:2:n-2
        s=s+2*f(a+i*h); %summation
    end
    
    %evaluate integral
    I=h/3*s;
    In(j) = I;
end
% plot(N,In);
% or
semilogx(N,In);
end