ABSTRACT
Among different numerical techniques for solving boundary and initial value problems, the finite difference methods are widely used. These methods are derived from the truncated Taylor’s series, also known as Taylor’s formula, where a given partial differential equation and the boundary and initial conditions are replaced by a set of algebraic equations that are then solved by various well-known numerical techniques. These methods have a significant advantage over other methods because of its simplicity of analysis and computer codes in solving problems with complex geometries. We will discuss difference schemes for first-and second-order partial derivatives, and then apply them to numerically solve boundary and initial value problems for second-order partial differential equations.
