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

  • Chawla M
  • Al-Zanaidi M
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Abstract

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

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Authors

  • M. M. Chawla

  • M. A. Al-Zanaidi

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