ABSTRACT
When a differential equation is solved analytically over a given region subject to specified boundary conditions, the resulting solution satisfies the differential equation at every point in the region. When the problem cannot be solved analytically or the analytic solution becomes so involved that numerical computation is very difficult, one generally resorts to a numerical technique for the solution. When finite-difference approach is used, the problem domain is discretized so that the values of the unknown dependent variable are considered only at a finite number of nodal points instead of every point over the region. If Ν nodes are chosen, Ν algebraic equations are developed by discretizing the governing differential equations and the boundary conditions for the problem. That is, the problem of solving the ordinary or partial differential equations over the problem domain is transformed to the task of development of a set of algebraic equations and their solution by a suitable algorithm.
