Simpson's 3/8th Rule MATLAB Program Example

Question


Evaluate the integral x^4 within limits -3 to 3 using Simpson's 3/8th Rule.

Solution


Let y(x)=x^4

here a=-3 and b=3

therefore (b-a)=6

let ‘n’ be the number of intervals. assume n=6 in this case.

also h=(b-a)/n = 6/6 =1

x: -3  -2  -1  0  1  2  3

y: 81  16  1  0  1  16  81

According to Simpson's 3/8th Rule:

answer= (3h/8)*[(y1+y7)+3*(y2+y3+y5+y6)+2*(y4)]

answer=(3/8)*[(81+81)+3*(16+1+1+16)+2*(0)]

answer=99.

MATLAB Code for Simpson's 3/8th Rule


%Created by myclassbook.org (Mayuresh)
%Created on 24 May 2013
%Question: Evaluate the integral x^4 within limits -3 to 3

clc;
clear all;
close all;

f=@(x)x^4; %Change here for different function
a=-3;b=3; %Given limits
n=b-a; %Number of intervals
h=(b-a)/n;
p=0;

for i=a:b
p=p+1;
x(p)=i;
y(p)=i^4; %Change here for different function
end

l=length(x);
x
y
answer=(3*h/8)*((y(1)+y(l))+3*(y(2)+y(3)+y(5)+y(6))+2*(y(4)))

Image Format








[caption id="" align="aligncenter" width="490"]MATLAB Program for Simpon's Three-Eighth Rule MATLAB Program for Simpon's Three-Eighth Rule[/caption]





Second Example


Evaluate the integral 1/(1+x) within limits 0 to 6 using Simpson's 3/8th rule.

Solution


Let y(x)=1/(1+x)

here a=0 and b=6

therefore (b-a)=6

let ‘n’ be the number of intervals. assume n=6 in this case.

also h=(b-a)/n = 6/6 =1

x: 0                  1                    2              3                  4               5               6

y: 1.0000   0.5000   0.3333   0.2500   0.2000   0.1667   0.1429

According to Simpson's 3/8th rule:

answer= (3h/8)*[(y1+y7)+3*(y2+y3+y5+y6)+2*(y4)]

answer=1.9660

MATLAB Code for Simpson's 3/8th Rule


%Created by myclassbook.org (Mayuresh)
%Created on 24 May 2013
%Question: Evaluate the integral 1/(1+x) within limits 0 to 6

clc;
clear all;
close all;

f=@(x)1/(1+x); %Change here for different function
a=0;b=6; %Given limits
n=b-a; %Number of intervals
h=(b-a)/n;
p=0;

for i=a:b
p=p+1;
x(p)=i;
y(p)=1/(1+i); %Change here for different function
end

l=length(x);
x
y
answer=(3*h/8)*((y(1)+y(l))+3*(y(2)+y(3)+y(5)+y(6))+2*(y(4)))

Image Format








[caption id="" align="aligncenter" width="490"]MATLAB Program for Simpon's Three-Eighth Rule MATLAB Program for Simpon's Three-Eighth Rule[/caption]





You may also like



If you like this article, please share it with your friends and like or facebook page for future updates. Subscribe to our newsletter to get notifications about our updates via email. If you have any queries, feel free to ask in the comments section below. Have a nice day!

Post a Comment

1 Comments