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


Projects by Yokesh R

Demo
Yokesh R · 2020-03-04 11:49:40

Hello Read more

Mixing tee project
Yokesh R · 2019-08-22 06:06:22

Case-1:       CASE-2:           CASE-3:         Read more

MAIN CODE: clear all close all clc A=[5 1 2 ; -3 9 4; 1 2 -7]; B=[10 ;-14; 33]; u = [0 1 2; 0 0 4; 0 0 0]; l = [0 0 0; -3 0 0; 1 2 0]; di = [5 0 0; 0 9 0; 0 0 -7]; mag = [0.25,0.5,0.75,1,1.5,2]; for i = 1 : length(mag) d = di*mag(i); Read more

DESCRIPTION: In this code, we are going to solve the two dimesnional convection equation defining a temperture distribution. The equation can be solved by 2 methods. 1. Implicit method 2. Explicit method In explicit method, we will be solving the equation sequencial Read more

DESCRIPTION: Using the central and skewed scheme methods initially, we have to develop the Taylor table, which should be converted into a matrix and solved for the constants. These constants help in solving the second order differential equation. Finally, the error res Read more

DESCRIPTION: In this code, we are going to compare the results of the 1D convection distribution equation describing the velocity for a range of time-step values. As a result, we will be getting the plots on the final velocity profile on time marching and computational Read more

DESCRIPTION:      Here in this code, we are using a range of dx terms for discretizing the first order derivative and studying the results of the dx vs error plot  CODE: clear all close all clc x = pi/3; dx = linspace(pi/4,pi/4000,30); %y Read more

STOICHIOMETRIC COMBUSTION   DESCRIPTION:   Stoichiometric combustion defines the ideal combustion that needs to take place for a given chemical equation. This is actually the general form of equation for alkanes. The general form might differ for e Read more

DESCRIPTION:         In this report, we will be studying the effects of the grid points in the first order convection equation describing one dimensional velocity distribution.   `frac{delu}{delt} = c*frac{delu}{delx}`   CODE: cl Read more


Loading...

The End