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Weighted finite difference techniques for the one-dimensional advection-diffusion equation. (English) Zbl 1034.65069

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 R. F. Warming and 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:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Citations:

Zbl 0291.65023
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References:

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