Discretization basics Numerical derivative vs. exact derivative

Objective: To solve steady and unsteady 2D heat conduction equation using different iterative techniques for implicit and explicit methods in MATLAB.   Introduction:   Assumptions: - The domain is a square domain - Number of points along the 'x-direction' is equal to the number of points along the 'y-direction'…

Objective: Write a MATLAB Code and to solve 1D linear equation Given Data:    Length( `L` ) = 1m                     Convective Coeffieient( `C` ) = 1 Time step( `dt` ) = 0.01 Grid point( `n` ) = [20,40,80,160]…

Objective: To write a MATLAB program that solves a 1D Linear equation for various time-steps. Given Data:    Length( `L` ) = 1m                     Convective Coeffieient( `C` ) = 1 Time step( `dt` ) = (1e-1,1e-2,1e-3,1e-4)…

Objective: Write a program that compares the first, second and fourth-order approximations of the first derivative against the analytical/exact derivative.   Given Function : `f(x) = sin(x)/x^3` First derivative of the function is `f'(x) = (x^3 cos(x) - sin(x)*3x^2)/x^6` The function is computed at `x = pi/3` First-order…

Objective: To derive the fourth-order approximation for the second-order derivative using  Central Differencing method  Skewed-right sided difference  Skewed-left sided difference Also, to write a MATLAB program and compute the second-order derivative of the analytical function exp(x)*cos(x) and compare…

Objective: To simulate the motion of a simple pendulum using MATLAB by solving a second-order ODE that represents a simple pendulum with damping. Introduction:  In engineering, ODE's usually describes the behaviour of a system. In this case, our ODE describes the transient behaviour of the simple pendulum. A simple…

Objective : To show a plot that compares the effect of the number of moles of carbon [`n`] on the stoichiometric coefficient [`ar`] and compare its trend changes with fuels [Alane, Alkene and Alkyne].   Introduction : Stoichiometric combustion is a concept where the concepts of combustion are easy to understand. When…