A repository of past Partial Differential Equation projects. Intro to PDES projects 1-3 were completed in MATLAB in 2018 for the Imperial introduction to computational PDE's course.

Intro to PDE's Project 1 2018

• Implemented Centered Finite difference method on a linked diffusion system in polar coordinates.
• Example contour graphs shown below for some fixed times.

Intro to PDE's Project 2 2018

Project was concerned with numerically solving equations of the form on a uniform rectangular grid:

• Numerical Solutions for equation (1) were achieved by using a Centred Finite Difference Method along with Gauss Seidel and Multi-Grid method to improve convergence.
• Numerical Solutions for equation (10) were achieved by using a Centred Finite Difference and Crank Nicolson Method along with an altered Gauss Seidel and Multi-Grid methods to improve convergence.
• Below is an example simulation with a known solution for error comparison.

Intro to PDE's Project 3 2018

Project focused on the solving of Turing Systems with Neumann BC shown below using similar methods to Project 2 with a focus on stabilty analysis and non-regular domains:

For example the Gauss Seidel step now solves the following:

• The graphs below show how the numerical simulation can generate a spots pattern which can typically be seen on animals. This was done via domain decomposition.

• The graph below shows a stripes pattern and spots pattern with their relative stabilities.