Comparision of the first second and fourth order approximations of the first derivative against the analytical solution for various values of dx

Aim: In this particular challenge, I am going to look at the effect of the time step on the solution of a 1D-linear convection equation.  Governing Equations and discretization: To solve the equation: Since the value of C is assumed to be a constant, the above equation is a linear in character. The time derivative…

Objective: In this challenge I am going to look at the effect of the number of grid points on the solution of a 1D-Linear convection equation.   An explicit scheme was used to discretize the governing equation. Since the chosen scheme was explicit, problem of instability comes into picture. From von-neumann stability…

In general , If we want a \'q\'th order approximation of a \'p\'th order derivative than there are p+q terms in the equation if we use one sided formula & p+q-1 terms in the equation if we use a central difference problem. Therefore second order derivative at a point for a  Skewed right sided difference is given…

%NOTE: If the plots and images are not visible on this page, please find them in the following google drive link "https://drive.google.com/open?id=1zBJd_e2mmHOVV5MvXfp4oC2eI1jUPyJG' Link is not opening by clicking, Copy and paste the link in the browser  AIM: To write a program in MATLAB for solving the quasi one…

Aim: To obtain the angular displacement of a simple pendulum as a function of time for the given damping factor and length. Problem Setup: The governing equation to be solved is given by  In the above equation,  b=damping factor m= mass of the ball in kg. L=1 metre m=1 kg b=0.5. g=9.81 m/s2. The given second-order…

Objective: In this assignment, finite difference method was used to discretize the first-order derivative to the desired order of accuracy, and the results obtained through their implementation were compared with the exact solution.  Given Function: Exact Derivative: The Exact and numerical Solutions of the given…

Aim: To discretize the 2-D steady heat conduction equation using the finite difference method and compare the solutions obtained using jacobi, gauss siedal and successive over relaxation methods. Problem setup : 1) Domain is square in shape, with a length of 1 meter. At time t=0, it is subjected to the following boundary…

Aim:To discretize the 2-D transient heat conduction equation using the finite difference method and solve the resulting algebraic equations using jacobi,gauss-siedal and SOR methods. Problem setup : 1) Domain is square in shape, with a length of 1 meter. At some time t=k, it is subjected to the following boundary conditions.…

Objective: The objective of the present assignment is to find out the numerical derivative of the given function  by the use of first order, second order, and fourth order approximations at various values of dx and compare the results obtained with the actual derivative. In this assignment I have computed the analytical…

If the flow is laminar, we have to solve the Continuity & Navier Stokes Equations in order to get the fluid flow distribution. Once we know the Fluid flow distribution we can find out the quantities like drag,lift,etc.. The Equations to be solved are the same no matter what the geometry is. But what makes the flow…

Hydrocarbons like alkanes , alkenes , and alkynes are mainly used as fuels as they have very high calorific values. Combustion of these fuels in lesser amount of air produces various toxic gases. Therefore right amount of air called the stoichiometric quantity should be provided for proper combustion of fuels. Simple Stoichiometric…

1)A=[1,2,3,4,5] gives us a row vector with 5 colums. The dimension of the matrix obtained has a dimension 1x5 2)The output of the second command gives a column matrix with5 rows and sigle column i.e., 5x1 3)We donot get any output with the following command as we cannot multiply a row vector with another row vector 4)In…