Fourth order operator splitting method for the three space parabolic equation with variable coefficients

Abstract

This paper deals with two new compact difference methods of 0(k ² + kh ² + h ⁴) for solving the system of general three space non-linear parabolic equations subject to the appropriate initial and Dirichlet boundary conditions using 27 and 19 spatial grid points in the presence and absence of mixed derivative terms, respectively. We also discuss the fourth order operator splitting method for the linear equation when applied to the proposed difference method. Various numerical examples including 3-space unsteady Navier-Stokes equations are provided which demonstrate the effectiveness and the computational efficiency of the methods developed.

Keywords:

• Nonlinear equations
• difference methods
• 3-D parabolic equations
• variable coefficients
• operator splitting method
• Navier-Stokes equations

C.R Categories:

• G.1.8

^∗ Present address: Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi,Delhi- 110 007, INDIA.

^∗ Present address: Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi,Delhi- 110 007, INDIA.

Notes

^∗ Present address: Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi,Delhi- 110 007, INDIA.