Higher order ADI method with completed Richardson extrapolation for solving unsteady convection–diffusion equations

A CCD-ADI method for unsteady convection-diffusion equations

With a combined compact difference scheme for the spatial discretization and the CrankNicolson scheme for the temporal discretization, respectively, a high-order alternating direction implicit method (ADI) is proposed for solving unsteady two dimensional convectiondiffusion equations. The method is sixth-order accurate in space and second-order accurate in time. The resulting matrix at each ADI...

A rational high-order compact ADI method for unsteady convection-diffusion equations

Article history: Received 30 October 2009 Received in revised form 17 October 2010 Accepted 12 November 2010 Available online 19 November 2010

A high-order Padé ADI method for unsteady convection-diffusion equations

ADI schemes for higher-order nonlinear diffusion equations

Alternating Direction Implicit (ADI) schemes are constructed for the solution of two-dimensional higher-order linear and nonlinear diffusion equations, particularly including the fourth-order thin film equation for surface tension driven fluid flows. First and second-order accurate schemes are derived via approximate factorization of the evolution equations. This approach is combined with itera...

A SIXTH ORDER METHOD FOR SOLVING NONLINEAR EQUATIONS

In this paper, we present a new iterative method with order of convergence eighth for solving nonlinear equations. Periteration this method requires three evaluations of the function and one evaluation of its first derivative. A general error analysis providing the eighth order of convergence is given. Several numerical examples are given to illustrate the efficiency and performance of the new ...