Our aim for the challenge is to derive 4th order approximation of 2nd order derivative using central difference, skewed right sided difference and skewed left sided difference. we also need to find 2nd order derivative of analytical function exp(x)*cos(x). Discritization: Numerical discritization is the technique which…

In Engineering, ODE is used to describe the transient behavior of a system.  A simple example is a pendulum   The way the pendulum moves depends on the Newtons second law. When this law is written down, we get a second order Ordinary Differential Equation that describes the position of the "ball" w.r.t time. …

The 2d heat conduction equation is `(delT)/(delt)+alpha*((del^2T)/(delx)+(del^2T)/(dely))=0` T=temperature along x and y direction, t=time, aplha=thermal diffusivity. A) Steady State : let us first consider the 2D state state part of equation : (del^2T)/(delx)+(del^2T)/(dely)=0' The steady state 2D heat conduction…

Aim : Simulation of 1D supersonic nozzle flow simulation using Macormack Method   Macormack's mathod: The MacCormack method is a variation of the two step Lax Wendroff scheme but is much simpler in application. To illustrate the algorithm, consider the following first order hyperbolic equation The application…