Splitting time methods and one dimensional special meshes for reaction-diffusion parabolic problems

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1196, Issue , 1997, Pages 106-113

  Clavero, C ^a   Jorge, J C ^b   Lisbona, F ^a   Shishkin, G I ^c  

^a UNIVERSITY OF ZARAGOZA   (Spain)

^b PUBLIC UNIVERSITY OF NAVARRE   (Spain)

^c INSTITUTE OF MATHEMATICS AND MECHANICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION IN LIQUIDS; FINITE DIFFERENCE METHOD;

ALTERNATING DIRECTIONS; CENTRAL FINITE DIFFERENCE; DIFFUSION PARAMETERS; PARABOLIC PROBLEMS; PIECEWISE UNIFORM MESH; REACTION DIFFUSION; TWO-DIMENSIONAL PROBLEM; UNIFORMLY CONVERGENT;

NUMERICAL METHODS;

EID: 21744459482     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-62598-4_84     Document Type: Conference Paper

References (10)

1. Clavero, C, Jorge, J.C., Lisbona, F.: Uniformly convergent schemes for singular perturbation problems combining alternating directions and exponential fitting techniques. In Applications of Avanced Computational Methods for Boundary and Interior Layers (J.J.H. Miller, Ed). Boole Press. Dublin (1993) 33-52
2. Farrell, P.A.: Sufficient conditions for uniform convergence of a class of difference schemes for a singularly perturbed problem. IMA J. Numer. Anal. 7 (1987) 459-472
3. Hegarty, A.F., Miller, J.J.H., O’Riordan, E., Shishkin, G.I.: Special numerical meth­ods for convection-dominated laminar flows at arbitrary Reynolds number. East-West J. Numer. Math. 2 (1994) 65-74
4. Hegarty, A.F., Miller, J.J.H., O’Riordan, E., Shishkin, G.I.: Special meshes for finite difference approximations to an advection-diffusion equation with parabolic layers. J. Comp. Phys. 117 (1995) 47-54
5. Herceg, D.: Uniform fourth order difference scheme for a singular perturbation problem. Numer. Math. 56 (1990) 675-693
6. Jorge, J. C, Lisbona, F.: Contractivity results for alternating direction schemes in Hilbert spaces. App. Numer. Math. 15 (1994) 65-75
7. Kellogg, R.B., Tsan, A.: Analysis of some difference approximations for a singular perturbation problem without turning points. Math. Comp. 32 (1978) 1025-1039
8. Shishkin, G.I.: Grid pproximation of singularly perturbed boundary value problems with convective terms. Sov. J. Numer. Anal. Math. Modelling 5 (1990) 173-187
9. Shishkin, G.I.: Grid approximations of singularly perturbed elliptic and parabolic equations (in Russian). Russian Academy Science, Ural Branch, Ekaterinburg (1992)
10. Stynes M., Roos, H.G.: The Midpoint Upwind Scheme. Preprint of Dep. of Math., University College, Cork (1996)