Partial differential equations (PDEs) arise, in general, in connection with phenomena taking place in continuous systems, in which, the quantities vary in space and time. The aimed processes show a wide diversity-heat andmass transport, propagation ofmechanical, electromagnetic, or quantummechanical waves and so on. Apart from a relatively small number of simple cases, in which the solutions can be expressed in closed form, it is necessary to resort to numerical methods to solve the underlying equations.