An extended trapezoidal formula for the diffusion equation in two space dimensions

  • Chawla M
  • Al-Zanaidi M
  • 3


    Mendeley users who have this article in their library.
  • 4


    Citations of this article.


We describe a locally one-dimensional (LOD) time integration scheme for the diffusion equation in two space dimensions: ut = v(uxx + uyy), based on the extended trapezoidal formula (ETF). The resulting LOD-ETF scheme is third order in time and is unconditionally stable. We describe the scheme for both Dirichlet and Neumann boundary conditions. We then extend the LOD-ETF scheme for nonlinear reaction-diffusion equations and for the convection-diffusion equation in two space dimensions. Numerical experiments are given to illustrate the obtained scheme and to compare its performance with the better-known LOD Crank-Nicolson scheme. While the LOD Crank-Nicolson scheme can give unwanted oscillations in the computed solution, our present LOD-ETF scheme provides both stable and accurate approximations for the true solution. © 2001 Elsevier Science Ltd.

Author-supplied keywords

  • Crank-Nicolson scheme
  • Diffusion equation
  • Extended trapezoidal formula
  • Nonlinear reaction-diffusion equations
  • Two space dimensions
  • Unconditional stability

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document


  • M. M. Chawla

  • M. A. Al-Zanaidi

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free