Diffusion Equation

Method of lines is a numerical technique used to solve a large class of partial differential equations (PDEs). Method to lines uses finite differences methods by discretising all spatial variables of a PDE while time remains continuous. This results in a system of ordinary differential equations (ODEs) which can be solve numerically using solvers such as ode15s() in Matlab. One prime example of a PDE encountered by many undergraduate students is the diffusion equation....

Cellular automata (CA) is a interesting mathematical tool that is used to model many natural phenomena such as biological behaviors. One prime example of CA models is it’s use in mathematical biology to model cellular interactions and behaviors by studying cells on a molecular level. In a CA model an individual square may represent a cell or particle on a grid/lattice. These elements can only take up a discrete number of states such as on or off and in a biological sense this can be interpreted as alive or empty....