An extended trapezoidal formula for the diffusion equation in two space dimensions
In: Computers & Mathematics with Applications, Jg. 42 (2001-07-01), S. 157-168
Online
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Zugriff:
We describe a locally one-dimensional (LOD) time integration scheme for the diffusion equation in two space dimensions: ut = ν(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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An extended trapezoidal formula for the diffusion equation in two space dimensions
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Autor/in / Beteiligte Person: | Al-Zanaidi, Mansour ; Chawla, M. M. |
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Zeitschrift: | Computers & Mathematics with Applications, Jg. 42 (2001-07-01), S. 157-168 |
Veröffentlichung: | Elsevier BV, 2001 |
Medientyp: | unknown |
ISSN: | 0898-1221 (print) |
DOI: | 10.1016/s0898-1221(01)00140-7 |
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