ABSTRACT

The partial differential equations are characterised by the fact that they involve more than one independent variables with respect to which partial derivatives of one or more dependent variables appear in the equation. The equation to a curve, no matter whether it is given in the implicit or the explicit function form, gives rise to a differential equation through differentiation and elimination of arbitrary constant(s) involved. A mathematical model representing a physical process should have three main features. A solution satisfying the given initial conditions must exist. Each set of initial conditions leads to a unique solution. Hence two solutions which obey the same initial conditions are identical. The solutions depend continuously on the initial conditions.