Higher Order Approximations using SKEWED AND SYMMETRIC STENCILS

OBJECTIVE: Solving the 2D heat conduction equation for steady and unsteady states. For the Steady state, we have to solve it using three iterative approaches namely,  1. Jacobi Method 2. Gauss-Seidel Method 3. Successive Over Relaxation Method. For the Transient state, we have to solve it using…

AIM :- To write a Matlab code for calculating the drag force against a cyclist and plot a graph between 1.)Velocity vs Drag force  2.)Drag Co-efficient vs Drag force THEORY:-  A drag force is the resistance force caused by the motion of a body through a fluid, such as water or air. A drag force acts opposite…

  AIM:- Matlab code to perform one-dimensional linear convection. THEORY:- The differential form of the General Convection diffusion equation is  `rho*(partialu)/(partialt) + rhov.nablau = nabla.(krhonablau)+Qv + nabla.Qs` Assuming constant density and constant diffusivity coefficients, absence of source…

Aim:-  Matlab program to simulate the pendulum motion (2nd order ode) Theory:- A pendulum is a body suspended from a fixed support so that it swings freely back and forth under the influence of gravity. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring…

LINEAR ONE-DIMENSIONAL CONVECTION EQUATION: `(partialu)/(partialt)+a*(partialu)/(partialx) = 0` where u(x,t) is the unknown function of (x,t) and a the convection speed.we can rewrite it as `u_t + a*u_x = 0` this equation has to be substantiated by the following initial and boundary conditions, for a>0: At t =…

Stoichiometric or Theoretical Combustion is the ideal combustin process where fuel is burned completely.  A complete combustion is a process burning all the carbon (`C`) to  (`CO_2`), all the hydrogen (`H`) to (`H_2O`)  With unburned components in the exhaust gas such as `C`, `H_2`, `CO` the combustion…

AIM:- To write a MATLAB program that compares the first, second and fourth order approximations of the first derivative against the analytical or exact derivative. THEORY:-   FINITE DIFFERENCE METHOD (FDM): -  FDM is a method used for solving the differential equations, in which finite differences approximate …

AIM: To write a MATLAB code which shows the effect of dx on error MAIN CODE:- %% % code to find the Effect of error on dx x = pi/3; dx = linspace(pi/40, pi/4000, 10); first_order_error = zeros(1,10); second_order_error = zeros(1,10); Fourth_order_error = zeros(1,10); for i = 1:length(dx) first_order_error(i) = first_order_approximation(x,dx(i));…

AIM:- Write a MATLAB code to compute 4th order approximations of the Second order derivative of CENTRAL DIFFERENCE, SKEWED RIGHT SIDED and SKEWED LEFT SIDED DIFFERENCE. THEORY: Analytical Function - `e^x*cos(x)` The Second order derivative of the analytical function is   `-2*e^(x)*sinx` CENTRAL DIFFERENCE…

DYNAMIC VISCOSITY :  Dynamic viscosity is the tangential force per unit area required to move one horizontal plane with respect to an other plane at an unit velocity when maintaining an unit distance apart in the fluid. Dynamic viscosity is expressed as `mu = tau*dy/(dc)` `mu = tau/y`  where  `tau` = shearing…

A partial differential equation (PDE) is an equation for some quantity `u` (dependent variable) which depends on the independent variables `x_1, x_2, x_3...,x_n` and involves derivatives of `u` with respect to at least some of the independent variables. In application `x_i` are often space…

1. The no. of coordinates that are needed to describe the relative movement permitted in a kinematic pair is defined as degrees of freedom. (or) the total no. of independent displacements or aspecTs of motion.2. A ball joint provides 3 degrees of freedom (i.e., 3 axis of rotational motion)3.Yes, in suspension we need 5…

A=[1 2 3] B=[1;2;3;]