comparison between the first, second and fourth order approximations of the first derivative against the analytical or exact derivative.

clear all close all clc %function = sin(x)/x^3 %derivative of function = (x^3*(cos(x) - sin(x)*3*x^2)/x^3 x = pi/3; dx = linspace(pi/4,pi/4000,20); for i = 1:length(dx) [first_order_error(i), second_order_error(i), fourth_order_error(i)] = all_approximations(x,dx(i)); end figure(1) loglog(dx,first_order_error,'color','r')…

Discretization is used to solve a partial differential function at discrete spoints in space. It basically converts a PDE into algebraic form using taylor series. clear all close all clc %function = sin(x)/x^3 %derivative of function = (x^3*(cos(x) - sin(x)*3*x^2)/x^3 x = pi/3; analytical_function = (x^3*(cos(x)) - sin(x)*3*x^2)/x^6…

https://projects.skill-lync.com/projects/optimizing-a-stalagmite-function-32889

Genetic Algorithm Genetic Algorithm (GA) is a branch of field of study called evolutionary comutation. It is based on evolution theory by Darwin. GA is used to optimize a given function to find its maximum or minimum value.  The basic components of a GA are 1. fitness function : It is the function that GA is trying…

clear all close all clc %importing the data data = load('data'); temp = data(:,1); cp = data(:,2); %plotting the original data figure(1) plot(temp,cp,'linewidth',3,'color','b') hold on xlabel('temperature') ylabel('specific heat') %curve fitting %assuming 2nd order equation. predicted_cp = aT + c co_efficients_1 = polyfit(temp,cp,1)…

https://projects.skill-lync.com/projects/solving-ODE-of-simple-pendulum-92272 the link to the challenge is attached above

`(d^2θ)/(dt^2)+(b/m)*(dθ)/(dt)+(g/l)*sinθ=0` The above ODE gives the motion of a simple pendulum. The second order ODE has to be convertedinto two first order ODE. consider θ= θ1 `(dθ)/(dt)=(dθ1)/(dt)=θ2`  `(d^2θ)/(dt^2)=(d^2θ1)/(dt^2)=(dθ2)/(dt)`…

clear all close all clc %state variables p1 = 101325 t1 = 500 t3 = 2300 g = 1.4 %engine parameters b = 0.1 s = 0.1 cr = 12 con= 0.2 % calculating swept_vol and clearance vol v_swept = (pi/4)*b^2*s v_clearance = v_swept/(cr-1) %state 1 v1= v_swept + v_clearance %stage 2 v2 = v_clearance % due to isentropic compression p1*v1^g=p2*v2^g…

  % program to calculate drag force for a bicycle clear all close all clc %drag force with variable velocity %inputs % drag coefficient c_d= 0.8; % frontal area area=0.5; % density of air density=1.225; % velocity of cyclist velocity= 1:50; %formula drag_force= density*area*velocity.*velocity*c_d*0.5; %plot to generate…

% forward kinematics of two arm robotic arm clear all close all clc %inputs l1= 2; l2=1; theta1= linspace(0,90,10); theta2= linspace(0,180,10); ct=1; %for loop for i= 1:length(theta1) th1= theta1(i); for j= 1:length(theta2) th2= theta2(j); % co ordinates of the two arm robotic arm x0= 0; y0= 0; x1= l1*cosd(th1); y1= l1*sind(th1);…

clear all close all clc % to create a row matrix a= [1 2 3 4] % to create a column matrix b= [1; 2; 3; 4;]