How to find the sum of values of a function at mid point of every subinterval?

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Mubashara Wali 2021-3-20

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https://ww2.mathworks.cn/matlabcentral/answers/778792-how-to-find-the-sum-of-values-of-a-function-at-mid-point-of-every-subinterval

评论： Mubashara Wali 2021-3-22

I am trying to run this code but don't know how to write code for finding value of function F at mid point of subinterval say, if my interval is [ti, ti+1] for i=0,1,2, n. and need to find sum of functional value at every (ti +ti+1)/2. I need to do it for Rsum2 in this code.

clc; clear all; format long
%%%%%%%%%%%%%%%%%%%%%%%%%%
alpha=0.8;% fractional index 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
TN=1      % time 
N=10
T0=0
tau=TN/N  
T=[T0:tau:TN]
X0=0
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
X(1)=X0
 
F =@(X,T)=X+T
 
for n=0:N-1
 
Rsum=0;
    for j=1:1:n+2
       Rsum=Rsum+2*F (j)
    end  
        
    Rsum2=0;
    for j=1:1:n+1
       Rsum2=Rsum2+4*F (j+1/2)
    end      
 
 X(n+2)=X(1) +(tau^alpha)*Rsum + (tau^alpha)*Rsum2
             
end
 

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Answer 1

Matt J 2021-3-20

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https://ww2.mathworks.cn/matlabcentral/answers/778792-how-to-find-the-sum-of-values-of-a-function-at-mid-point-of-every-subinterval#answer_653622

编辑：Matt J 2021-3-20

在 MATLAB Online 中打开

If your function is vectorized, like in the following example, it is quite simple:

fun=@(tm) tm.^2+ sqrt(tm); %A vectorized function
n=8;
t=sort(rand(1,n)) %interval end points t(i)
t = 1×8
    0.0157    0.1988    0.2703    0.3719    0.5549    0.6696    0.7340    0.7594
tmid = t(1:end-1)/2 +t(2:end)/2 %interval mid-points
tmid = 1×7
    0.1073    0.2345    0.3211    0.4634    0.6122    0.7018    0.7467
result =  sum(fun(tmid))
result = 6.3528

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Matt J 2021-3-22

You're welcome, but if it works, please Accept-click the answer.

Mubashara Wali 2021-3-22

Matt J Actually its working when F is a function of T only, but having a problem when F is a function of two independent variables as I mentioned in my code that F =@(X,T)=X+T. I would really appreciate if you can help me in this regard.

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