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

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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

採用された回答

Matt J
Matt J 2021 年 3 月 20 日
編集済み: Matt J 2021 年 3 月 20 日
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
  3 件のコメント
Mubashara Wali
Mubashara Wali 2021 年 3 月 22 日
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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