Convergence, Stability, and Consistency of Finite Difference Schemes in the Solution of Partial Differential Equations

A finite difference scheme is produced when the partial derivatives in the partial differential equation(s) governing a physical phenomenon are replaced by a finite difference approximation. The result is a single algebraic equation or a system of algebraic equations which, when solved, provide an approximation to the solution of the original partial differential equation at selected points of a solution grid. The solution grid (also referred to as computational grid or numerical grid) is originated by dividing the axes representing the independent variables in the solution domain into a number of intervals. The extreme points of the interval will represent points in the solution grid. If we draw lines perpendicular to a given axes passing through the extreme points of the intervals, the resulting grid is the computational grid.