ε-uniform schemes with high-order time-accuracy for parabolic singular perturbation problems

IMA Journal of Numerical Analysis

Volumn 20, Issue 1, 2000, Pages 99-121

  Hemker, P W ^a   Shishkin, G I ^b   Shishkina, L P ^c  

^a CWI   (Netherlands)

^b INSTITUTE OF MATHEMATICS AND MECHANICS   (Russian Federation)

^c Sci Res Inst of Heavy Mach Bldg   (Russian Federation)

Author keywords

Defect correction; Higher order time accuracy schemes; Parabolic pdes; uniform convergence

Indexed keywords

DISCRETE EVENT SIMULATION; MESH GENERATION;

DEFECT CORRECTION; DIFFERENCE APPROXIMATION; DISCRETE APPROXIMATION; DISCRETIZATION METHOD; HIGHER-ORDER; PARABOLIC PDES; SINGULAR PERTURBATION PROBLEMS; UNIFORM CONVERGENCE;

BOUNDARY LAYERS;

EID: 0034348728     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/20.1.99     Document Type: Article

References (15)

1. DOOLAN, E. P., MILLER, J. J. H., & SCHILDERS, W. H. A. 1980 Uniform Numerical Methods far Problems with Initial and Boundary Layers. Dublin: Boole.
2. FARRELL, P. A., HEMKER, P. W., & SHISHKIN, G. I. 1996a Discrete approximations for singularly perturbed boundary value problems with parabolic layers, I. J. Comput. Math. 14, 71-97.
3. FARRELL, P. A., HEMKER, P. W., & SHISHKIN, G. I. 1996b Discrete approximations for singularly perturbed boundary value problems with parabolic layers, II. J. Comput. Math. 14, 183-194.
4. FARRELL, P. A., HEMKER, P. W., & SHISHKIN, G. I. 1996c Discrete approximations for singularly perturbed boundary value problems with parabolic layers, III. J. Comput. Math. 14, 273-290.
5. FARRELL, P. A., MILLER, J. J. H., O'RIORDAN, E., & SHISHKIN, G. I. 1996d A uniformly convergent finite difference scheme for a singularly perturbed semilinear equation. SIAM J. Numer. Anal. 33, 1135-1149.
6. HEMKER, P. W. & SHISHKIN, G. I. 1994 On a class of singularly perturbed boundary value problems for which an adaptive mesh technique is necessary. Proc. Second Int. Colloquium on Numerical Analysis (D. Bainov and V. Covachev, eds). VSP, International Science Publishers, pp 83-92.
7. HEMKER, P. W., SHISHKIN, G. I., & SHISHKINA, L. P. 1997 The use of defect correction for the solution of parabolic singular perturbation problems. Z. Angewandte Mathematik Mechanik 76, 59-74.
8. LADYZHENSKAYA, O. A. & URAL'TSEVA, N. N. 1973 Linear and Quasi-Linear Equations of Elliptic Type. Moscow: Nauka (in Russian).
9. MILLER, J. J. H., O'RIORDAN, E., & SHISHKIN, G. I. 1996 Numerical Methods For Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions. Singapore: World Scientific,.
10. MORTON, K. W. 1996 Numerical Solution of Convection-Diffusion Problems, vol. 12 of Applied Mathematics and Mathematical Computation. London: Chapman and Hall.
11. ROOS, H.-G., STYNES, M., & TOBISKA, L. 1996 Numerical Methods for Singularly Perturbed Differential Equations: Convection-Diffusion and Flow Problems (Springer Series in Computational Mathematics 24). Berlin: Springer.
12. SAMARSKI, A. A. 1989 Theory of Difference Scheme. Moscow: Nauka (in Russian).
13. SHISHKIN, G. I. 1983 Difference scheme on a non-uniform grid for the differential equation with a small parameter at the highest derivative. Zh. Vychisl. Mat. Mat. Fiz. 23, 609-619 (in Russian).
14. SHISHKIN, G. I. 1987 Approximation of solutions to singularly perturbed boundary value problems with corner boundary layers. Zh. Vychisl. Mat. Mat. Fiz. 27, 1360-1374 (in Russian).
15. SHISHKIN, G. I. 1952 Mesh Approximation of Singularly Perturbed Elliptic and Parabolic Equations. Ekaterinburg: Ur. O. RAN (in Russian).