ABSTRACT

This chapter presents the finite difference method, which is classified as a discrete approximate solution technique. Rather than providing a continuous solution for the primary dependent variables defined throughout the domain O, discrete solution techniques yield approximations only at a specific number of locations. When necessary, intermediate values of the primary dependent variables and their derivatives can be computed from the discrete approximation by suitable interpolation techniques. The most commonly used discrete solution technique is the finite difference method. The finite difference method makes use of the Calculus of Finite Differences, in which derivatives are replaced by suitable difference formulas involving simple algebraic operations. Physical phenomena involving more than one independent variable are typically expressed using equations involving partial derivatives. The Calculus of Finite Differences can be used to obtain approximate solutions to partial differential equations that characterize specific boundary/initial value problems.