# Central Difference For Loop

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Robert Flores on 19 Mar 2019
Edited: KALYAN ACHARJYA on 19 Mar 2019
Hello, I am trying to use the central difference for the function sin(2*pi*x), centered around x=0.313. I know what value should be, that is my "act" variable. If someone can help me why my for loop is messed-up, it'll be much appreciated.
CODE:
clc, clear, close all
syms x
% Actual Value
f = sin(2*pi*x);
df = diff(f,x);
x = 0.313;
true_value = 2*pi*cos(2*pi*x)
% Central Difference
for i=1:3
x = 0.313;
for h = [0.01 0.1 0.25]
df_dx(i) = (sin(2*pi*(x+h))-sin(2*pi*(x-h)))/2*h
end
end
act = (sin(2*pi*0.314)-sin(2*pi*0.312))/0.02

KALYAN ACHARJYA on 19 Mar 2019
Edited: KALYAN ACHARJYA on 19 Mar 2019
-If someone can help me why my for loop is messed-up-
clc, clear, close all
syms x
% Actual Value
f=sin(2*pi*x);
df=diff(f,x);
x=0.313;
true_value=2*pi*cos(2*pi*x);
h=[0.01 0.1 0.25];
df_dx=zeros(1, length(h));
% Central Difference
for i=1:3
df_dx(i)=(sin(2*pi*(x+h(i)))-sin(2*pi*(x-h(i))))/2*h(i);
end
act=(sin(2*pi*0.314)-sin(2*pi*0.312))/0.02;
Output:
df_dx=
-0.0002 -0.0227 -0.0964
Without for loop
clc, clear, close all
syms x
% Actual Value
f=sin(2*pi*x);
df=diff(f,x);
x=0.313;
true_value=2*pi*cos(2*pi*x);
h=[0.01 0.1 0.25];
% Central Difference
df_dx=(sin(2*pi.*(x+h))-sin(2*pi.*(x-h)))./(2*h);
act=(sin(2*pi*0.314)-sin(2*pi*0.312))/0.02;
Command Window:
>> df_dx
df_dx =
-0.0002 -0.0227 -0.0964

madhan ravi on 19 Mar 2019
madhan ravi on 19 Mar 2019
./ is not corrected yet , please by any chance don't delete this answer so that it's pretty clear how many possible mistakes can be made in this problem.
KALYAN ACHARJYA on 19 Mar 2019
Yes, got it sir, but for small number of iterations, there may be negligible difference.right?
>> matlab_ans_march_19
Without Pre-allocation
Elapsed time is 0.003340 seconds.
%%
>> matlab_ans_march_19
With Pre-allocation
Elapsed time is 0.002957 seconds.
Yes, prefer to use for better coding performance (always).