The purpose of these lectures is to address deterministic numerical methods for PDEs and applications to modelling. This will include scalar hyperbolic, parabolic, linear and nonlinear parabolic PDEs. Several types of methods will be discussed, together stability, consistency and convergence issues.
Heat equation, Advection equation, Burgers equation, Fischer-KPP, Explicit/implicit methods, Central schemes, Upwind schemes, Numerical diffusion, Numerical dispersion.