Uniform Second-Order Hybrid Schemes on Bakhvalov-Shishkin Mesh for Quasi-Linear Convection-Diffusion Problems

Quan Zheng; Xue Zheng Li; Yu Feng Liu

doi:10.4028/www.scientific.net/AMR.871.135

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HomeAdvanced Materials ResearchAdvanced Materials Research Vol. 871Uniform Second-Order Hybrid Schemes on...

Uniform Second-Order Hybrid Schemes on Bakhvalov-Shishkin Mesh for Quasi-Linear Convection-Diffusion Problems

Abstract:

In this paper, we propose a class of hybrid difference schemes combining the central difference scheme and the midpoint upwind scheme on the Bakhvalov-Shishkin mesh for solving quasi-linear singularly perturbed convection-diffusion boundary value problems. Point-wise second-order convergence uniform in the perturbation is proved clearly by using the-stability. The numerical experiments support the schemes and the uniform second-order estimate.

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Periodical:

Advanced Materials Research (Volume 871)

Pages:

135-140

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.871.135

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Online since:

December 2013

Authors:

Quan Zheng*, Xue Zheng Li, Yu Feng Liu

Keywords:

Bakhvalov-Shishkin Mesh, Convection-Diffusion, Quasi-Linear ODE, Singularly Perturbed Problem, Uniform Convergence

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References

[1] J. Lorenz, Stability and monotonicity properties of stiff quasi-linear boundary problems. Univ. u Novom Sadu Zb. rad. Prir. -Mat. Fak. Ser. Mat., 12 (1982) 151-175.

Google Scholar

[2] R. E. O'Malley Jr., Introduction to Singular Perturbations. New York, London: Academic Press, (1974).

Google Scholar

[3] R. Vulanovi´c, A uniform numerical method for quasi-linear singular perturbation problems without turning points, Computing, 41 (1989) 97-106.

DOI: 10.1007/bf02238732

Google Scholar

[4] A.S. Bakhvalov, On the optimization of methods for solving boundary value problems with boundary layers, Zh. Vychisl. Mat. i Mat. Fiz. 9 (1969) 841-859 (in Russian).

Google Scholar

[5] G.I. Shishkin, Discrete Approximation of Singularly Perturbed Elliptic and Parabolic Equations, Russian Academy of Sciences, Ural Section, Ekaterinburg, 1992 (in Russian).

Google Scholar

[6] J.J.H. Miller, R.E. O'Riordan, G.I. Shishkin, Fitted Numerical Methods for Singular Perturbation Problems. World Scientific, Singapore, (1996).

Google Scholar

[7] H. -G. Roos, M. Stynes, L. Tobiska, Robust Numerical Methods for Singularly Perturbed Differential Equations, Springer-Verlag, Berlin, Heidelberg, (2008).

DOI: 10.1007/978-3-662-03206-0

Google Scholar

[8] M.K. Kadalbajoo, V. Gupta, A brief survey on numerical methods for solving singularly perturbed problems, Appl. Math. Comput. 217 (2010) 3641-3716.

DOI: 10.1016/j.amc.2010.09.059

Google Scholar

[9] T. Linß, H. -G. Ross, R. Vulanović, Unifrom point-wise convergence on Shishkin-type meshes for quasi-linear covection-diffusion problem, SIAM J. Numer. Anal., 38 (2000) 897-912.

DOI: 10.1137/s0036142999355957

Google Scholar

[10] T. Linß, Sufficient conditions for uniform convergence on layer-adapted grids, Applied Numerical Math., 37 (2001) 241-255.

DOI: 10.1016/s0168-9274(00)00043-x

Google Scholar

[11] T. Linß, Uniform second order point-wise convergence of a finite difference discretization for a quasi-linear problem Comput. Math. Math. Phys. 41 (2001) 898-909.

Google Scholar

[12] V.B. Andreev, N.V. Kopteva, On the convergence, uniform with respect to a small parameter, of monotone three-point difference schemes, Differ. Uravn., 34 (1998).

Google Scholar