## DISCRETIZATION OF FIRST ORDER DERIVATIVE USING FIRST, SECOND AND FOURTH ORDER APPX

DESCRIPTION:

In this code, we are going to discretize the function for the first-order derivative using first, second and fourth order approximation techniques and studying the error bounced by every method by a bar chart.

CODE:

clear all
close all
clc

x = pi/3;
dx = pi/100;

%y = (sinx)/(x^3)
%actual dy by equation
dy = (x^3 *cos(x) - 3*x^2 *sin(x))/x^6;

%first order appx by frwd method
dy1 = ((sin(x+dx)/(x+dx)^3) - (sin(x)/(x)^3))/(dx);

%second order appx by central method
dy2 = ((sin(x+dx)/(x+dx)^3) - (sin(x-dx)/(x-dx)^3))/(2*dx);

%fourth order appx
dy3 = ((sin(x-(2*dx))/(x-(2*dx))^3)-(8*(sin(x-dx)/(x-dx)^3))+(8*(sin(x+dx)/(x+dx)^3))-(sin(x+(2*dx))/(x+(2*dx))^3))/(12*dx);

error1 = abs(dy1- dy);
error2 = abs(dy2- dy);
error3 = abs(dy3- dy);

error = [error1,error2,error3];
bar(error)

title('DISCRETISATION BY RANGE OF dx TERMS')
xlabel('first order error  second order error  fourth order error')
ylabel('error')



PLOT:

RESULT:

ERROR 1 = 0.0756

ERROR2 = 0.00314

ERROR3 = 1.7e-5

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