Analytical Construction of Uniformly Convergent Method for Convection Diffusion Problem

Authors

  • Ali Filiz Department of Mathematics, Faculty of Science, Pamukkale University, Turkey

DOI:

https://doi.org/10.24203/ajfam.v9i3.6805

Keywords:

Local Green’s function, convection-diffusion problem, boundary value problem, boundary layer, singular points.

Abstract

In this paper, we study the uniformly convergent method on equidistant meshes for the convection-diffusion problem of type;

where   the formal adjoint operator of L.

Lu=-εu''+bu'+c u=f(x), u(0)=0, u(1)=0

At the end of the this paper we will generate the scheme;

-e^(ρ_i )/(e^(ρ_i )+1) U_(i-1)+U_i-1/(e^(ρ_i )+1) U_(i+1)=(f_i-c_i U_i ) h/b ((e^(ρ_i )-1)/(e^(ρ_i )+1))

References

Filiz A., Nesliturk, A. I. and Ekici, M., “An ε-uniform numerical method for a singularly-perturbated problem”, XXII Ulusal matematik sempozyumu, Sirince, Izmir, 2009.

Filiz A., “ε-uniform convergence for a boundary value problem”, XXIII Ulusal matematik sempozyumu, Erciyes Universitesi, Kayseri, 2010.

Miller, H. J. H., O’Riordan, E. and Shishkin, G. I., Fitted Numerical methods for singular perturbation problems: Error estimates in the maximum norm for linear problems in one and two dimensions, World Scientific, USA, 1996.

Roos, H. G., Ten Ways to Generate the Il’in and Related Schemes”, J. of Computational and Appl. Maths., 53 p. 43-59, 1994.

Roos, H. G., Stynes, M. and Tobiska, L., Numerical Methods for Singularly Perturbed Differential Equations, Convection Diffusion and Flow Problems, Springer−Verlag, Berlin Heidelbrg Newyork, 1994.

Roos, H. G., Stynes, M. and Tobiska, L., Robust Numerical Methods for Singularly Perturbed Differential Equations, Convection Diffusion and Flow Problems, 2008.

Stynes, M., Tobiska, L., “A finite difference analysis of a streamline diffusion method on a Shishkin mesh”, Numer Algoritms, 18(3-4), pp.337-360, 1998.

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Published

2021-12-31

How to Cite

Filiz, A. (2021). Analytical Construction of Uniformly Convergent Method for Convection Diffusion Problem. Asian Journal of Fuzzy and Applied Mathematics, 9(3). https://doi.org/10.24203/ajfam.v9i3.6805