A higher-order difference method for 3-D parabolic partial differential equations with nonlinear first derivative terms

Abstract

In this paper, we present a finite difference method of 0(k ² +kh ²+h ⁴) for the second order nonlinear 3-D parabolic partial differential equation v ₁ u _xx + v ₂ U _yy +v ₃ u _zz = f(x,y,z,t,u,u _x ,u _y ,u _z ,u _t ) where v _i , i=l, 2, 3 are positive constants, using 19 spatial grid points subject to Dirichlet boundary conditions. The unconditionally stable character of the difference scheme when applied to a linear diffusion-convection equation has been verified. Numerical examples are given to demonstrate the performance of the method derived.

Keywords:

• 3-D Parabolic partial differential equations
• linear diffusion-convection equation
• finite difference method
• operator splitting method
• stability analysis

^∗Present address: Vice-Chancellor, A.P.S. University, Rewa(M.P.), India 486001.

^∗Present address: Vice-Chancellor, A.P.S. University, Rewa(M.P.), India 486001.

Notes

^∗Present address: Vice-Chancellor, A.P.S. University, Rewa(M.P.), India 486001.