A study on finite difference method using explicit and monotone scheme hyperbolic partial differential equation

Abstract

All the problems almost in science and technology can be expressed mathematically in the form of partial differential equation. Mainly all the types of partial differential equation has a specific characters. Specially hyperbolic equation is associated with vibrations and sounds especially problems related to time, heat, diffusion and elasticity. In this paper, the author discussed the explicit and monotone scheme based on finite difference method to find the numerical solution of hyperbolic partial differential equation with linear advection equation and also discussed the upwind difference scheme which was extended to an monotone scheme.