ABSTRACT
This chapter utilizes method of lines (MoL) to solve parabolic and hyperbolic partial differential equations (PDEs) by converting them into a set of ordinary differential equations (ODEs). It discusses classification of first- and second-order PDEs and their implication for numerical solutions. This classification of PDEs will prove important for the selection of appropriate numerical techniques. PDF is discretized in the spatial domain using central difference formula and solved using MoL. Finite volume methods (FVM) are a different class of PDE solution techniques. Instead of discretizing the domain into various intervals and writing the differential equation in terms of variables at the nodes, the domain is discretized in finite volumes. The chapter also discusses several methods for using finite differences in time and space. Parabolic PDEs result most often when simulating processes with diffusive component in one direction. The chapter explores numerical methods to solve parabolic PDEs.
