Objective: Solving Quasi 1D Nozzle Flows through Conservative and Non-Conservative Methods. I\'ll also be focussing on the importance of grid number in the convergence also the computation time. (Theory - John D Anderson COMPUTATIONAL FLUID DYNAMICS) Physical Aspects and the Assumptions of the flow: We consider the steady,…

Background: The wider perspective is to solve the 1-dimensional linear convection equation. This comes from the two-dimensional momentum equation assuming the same shape to make it a simpler PDE.  `(∂u)/(∂t)+c(∂u)/(∂x)=0` Aim: Our objective is to solve the PDE through MatLab code and compare the…

Solving a Linear System Equations: AX = B through Jacobi. Gauss-Seidel and SOR Methods Objectives of the Project: 1) Determining Eigenvalues, Spectral Radius of an iteration matrix 2) Solve the X Matrix through three solving methods 3) Establishing the relationship between the Spectral radius and convergence of the solver.…

Title: Comparison of the first, second and fourth-order error approximations for first-order differential equation Initially, the problem solving started with giving input variables. There are two variables x and dx while I assumed `x=pi/3` (a constant value). 'dx' is a variable in this comparison project. So, I have…

Title: Deriving the fourth-order approximation for second-order derivative through the central, skewed right and skewed left differencing schemes. Subsequently evaluating their errors Function: `exp(x)*cos(x)` Firstly, Central differencing derivation through Taylor table Here You get 5 equations and we have 5…

To write a program that could solve the second-order ode through 'ode' function. The equation which needs to be solved is    `(d^2theta)/(dt^2) + (b/m)(d(theta))/dt +(g/l)sintheta = 0` where theta is angular displacement b = dampingm = massg = gravityl = lengthIt is given that, initial angular velocity is = 3…

Thie task is to solve 2D Heat Conduction equation  `(del T)/(del t) = ((del^2T)/(del x^2) +(del^2T)/(del x^2))*K` where K is the thermal diffusivity Assumptions in the equation: Internal heat generation is zero which implies a change of heat flow from one to another side is converted into internal energy. Abstract:…

The Project aims to show two things 1)  error of first order, second order and fourth order with analytical derivative 2)  comparison in between different order approximations 1-Step: Initially, the code started with inputting variables x and dx while x value has been mentioned in the question as pi/3. While…