I don't the error statement.

clc;

clear;

close all;

Vmax = 50; %% m/s

R = 0.25; %% m

%% Equation is: v(r)= vmax*(R-r^2)^(cos(r)/8)

Vavg = @(r) 2/(R^2).*Vmax.*((R-r.^2)).^(cos(r)/8).*r; %% m/s %% function handle

Vavg = integral(Vavg,0,R); %% integral of V

Vavg_exact = 41.4592; %% m/s %% result from WolframAlpha

%% Compound Midpoint Method

% mp= (s(i)+s(i+1))/(2) %% eqn of midpoint

% h= s(i+1),-s(i)

dif = 1;

n = 1;

while dif > 0.01

s = linspace(0,R,n + 1);

out = 0; % holder

for i = 1:n

mp_approx = (2./(R^2).*Vmax.*(R-((s(i)+s(i+1))./2).^2).^(cos((s(i)+s(i+1))./2)/8).*((s(i)+s(i+1))./2)).*(s(i+1)-s(i));

out = out + mp_approx;

end

dif = abs(Vavg - out);

n = n + 1;

end

subp_mp = n - 1; % subpoint of midpoint approximation

%% Compound Trapezoidal Method

dif = 1;

n = 1;

while dif > 0.01

s = linspace(0,R,n + 1);

out = 0;

for i = 1:n

trap = ((2./(R^2).*Vmax.*((R-s(i).^2)).^(cos(s(i))/8).*s(i))+(2./(R^2).*Vmax.*(R-s(i+1).^2).^(cos(s(i+1))/8).*s(i+1))).*(s(i+1)-s(i))./2;

out = out + trap;

end

dif = abs(Vavg - out);

n = n + 1;

end

subp_trap = n - 1;

%% Simpson's Method

dif = 1;

n = 1;

while dif > 0.01

s = linspace(0,R,n + 1);

out = 0;

for i = 1:n

simp = ((2./(R^2).*Vmax.*((R-s(i).^2)).^(cos(s(i))/8).*s(i))+4*(2./(R^2).*Vmax.*(R-s(i+1).^2).^(cos(s(1+i))/8).*(s(1+i)))+(2./(R^2).*Vmax.*(R-s(2+i).^2).^(cos(s(2+i))/8).*s(2+i))).*(s(2+i)-s(i))./6;

out = out + simp;

end

dif = abs(Vavg - out);

n = n + 1;

end

subp_simp = n - 1;

The error i get is;

Index exceeds the number of array elements. Index must not exceed 2.

Error in BarisMenemenlioglu_HW4 (line 55)

simp = ((2./(R^2).*Vmax.*((R-s(i).^2)).^(cos(s(i))/8).*s(i))+4*(2./(R^2).*Vmax.*(R-s(i+1).^2).^(cos(s(1+i))/8).*(s(1+i)))+(2./(R^2).*Vmax.*(R-s(2+i).^2).^(cos(s(2+i))/8).*s(2+i))).*(s(2+i)-s(i))./6;

I don't really understand what's the problem.

[Dave B]

you're referencing s(2+i)but you made s exactly n+1 elements big. You're looping until n, so when i is exactly n you're pointing to s(2+n) but s is n+1 elements big. Your index (2+i) exceeds the number of array elements (1+i)

Answer 1

[Bhanu Prakash]

Hi Baris,

As per my understanding, you are trying to perform some analysis using Simpson’s method but are facing an error during execution.

The reason for the error could be improper indexing of the array “s”. The array “s” has only two elements in it and the code is trying to access the third element of this array, which is not present. So, it is throwing an error.

A possible solution to avoid this error is to change the parameters in “linspace” for “s” to contain three elements.

You can access the following documentation of “linspace”:

Generate linearly spaced vector - MATLAB linspace - MathWorks India

Hope this answer helps you.

Thanks,

Bhanu Prakash.