Chapter 8
Deterministic Dynamical Systems
Section 3
Simulating a Partial Differential Equation
Partial Differential Equations (PDEs) describe the evolution of dynamical systems involving both time and space. Examples in physics include sound, heat, electromagnetism, fluid flow, and elasticity, among others. Examples in biology include tumor growth, population dynamics, and epidemic propagations. PDEs are hard to solve analytically. Therefore, PDEs are often studied via numerical simulations. In this section, we will illustrate how to simulate a reaction-diffusion system described by a PDE called the FitzHugh–Nagumo equation.