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
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