Understanding Linear Systems

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,…

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.…

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:…

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…

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…

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…