An efficient higher order compact finite difference schemes for linear hyperbolic partial differential equations

Abstract

To approximate the partial derivative of Linear Hyperbolic Partial Differential Equations (LPHDE), a system of compact schemes used at non-boundary nodes. For the spatial discretization of the advection term, instead of using the upwind schemes, central difference based compact 4th order and conventional 2nd order schemes are experimented. The main aim of the numerical experiments carried out is, to assess the ability of the compact 4th order scheme in capturing the convection process, in comparison with the conventional 2nd order scheme.