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

✍ Scribed by M.M. Chawla; M.A. Al-Zanaidi

Book ID: 104352151
Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 493 KB
Volume: 42
Category: Article
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(01)00140-7

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✦ Synopsis

We describe a locally one-dimensional (LOD) time integration scheme for the diffusion equation in two space dimensions: ut = u(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.

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