A Numerical Method for Viscous Flow Using Third Order Upwind Differencing

A new method is proposed for solving the initial value problem of a partial differential equation with both convective (hyperbolic) and diffusive (parabolic) term. The hyperbolic and parabolic term are approximated by the third order upwind and second order central difference method respectively. The resulting set of ODEs are solved by the third order Adams-Bashforth method. Linear stability analysis is performed and the amplification factor is examined.