(Science International,27(3), 2015) Muhammad Farhan Tabassum
In this paper we investigate the quantitative behavior of a wide range of numerical methods for solving linear partial
differential equations [PDE’s]. In order to study the properties of the numerical solutions, such as accuracy, consistency, and stability, we use
the method of modified equation, which is an effective approach. To determine the necessary and sufficient conditions for computing the
stability, we use a truncated version of modified equation which helps us in a better way to look into the nature of dispersive as well as
dissipative errors. The Wave Equation arises in the construction of characteristic surfaces for hyperbolic partial differential equations, in the
calculus of variations, in some geometrical problems and in simple modals for gas dynamics, whose solution involves the method of
characteristics. Accuracy and stability of Upstream Scheme is checked by using Modified Differential Equations [MDE’s].