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Zbl 1034.65069
Dehghan, Mehdi
Weighted finite difference techniques for the one-dimensional advection-diffusion equation. (English)
[J] Appl. Math. Comput. 147, No. 2, 307-319 (2004). ISSN 0096-3003

Summary: Various numerical techniques are developed and compared for solving the one-dimensional advection--diffusion equation with constant coefficient. These techniques are based on the two-level finite difference approximations. The basis of analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach, developed by {\it R. F. Warming} and {\it B. J. Hyett} [J. Comput. Phys. 14, 159--179 (1974; Zbl 0291.65023)]. This allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference schemes. The new methods are more accurate and are more efficient than the conventional techniques. These schemes are free of numerical diffusion. The results of a numerical experiment are presented, and the accuracy and central processor (CPU) time needed are discussed and compared.

MSC 2000:: *65M06 Finite difference methods (IVP of PDE)
35K15 Second order parabolic equations, initial value problems
65M12 Stability and convergence of numerical methods (IVP of PDE)

Keywords: Two-level finite difference techniques; Advection-diffusion processes; Numerical differentiation; Implicit schemes; numerical experiment; Stability; Explicit methods

Citations: Zbl 0291.65023

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Zentralblatt MATH Berlin [Germany]