scholarly journals A Recent Development of Numerical Methods for Solving Convection-Diffusion Problems

2012 ◽  
Vol 1 (1) ◽  
pp. 1-12 ◽  
Author(s):  
A. Shukla ◽  
A. K. Singh ◽  
P. Singh
Keyword(s):  
Numerical Methods ◽  
Convection Diffusion ◽  
Diffusion Problems

scholarly journals ROBUST NOVEL HIGH-ORDER ACCURATE NUMERICAL METHODS FOR SINGULARLY PERTURBED CONVECTION‐DIFFUSION PROBLEMS

2005 ◽  
Vol 10 (4) ◽  
pp. 393-412 ◽  
Author(s):  
G. I. Shishkin
Keyword(s):  
Numerical Methods ◽  
Order Of Convergence ◽  
Diffusion Problem ◽  
Singularly Perturbed ◽  
Order Of Accuracy ◽  
Convection Diffusion ◽  
Expansion Technique ◽  
Uniformly Convergent ◽  
Problem Data ◽  
Diffusion Problems

For singularly perturbed boundary value problems, numerical methods convergent ϵ‐uniformly have the low accuracy. So, for parabolic convection‐diffusion problem the order of convergence does not exceed one even if the problem data are sufficiently smooth. However, already for piecewise smooth initial data this order is not higher than 1/2. For problems of such type, using newly developed methods such as the method based on the asymptotic expansion technique and the method of the additive splitting of singularities, we construct ϵ‐uniformly convergent schemes with improved order of accuracy. Straipsnyje nagrinejami nedidelio tikslumo ϵ‐tolygiai konvertuojantys skaitmeniniai metodai, singuliariai sutrikdytiems kraštiniams uždaviniams. Paraboliniam konvekcijos‐difuzijos uždaviniui konvergavimo eile neviršija vienos antrosios, jeigu uždavinio duomenys yra pakankamai glodūs. Tačiau trūkiems pradiniams duomenims eile yra ne aukštesne už 2−1. Šio tipo uždaviniams, naudojant naujai išvestus metodus, darbe sukonstruotos ϵ‐tolygiai konvertuojančios schemos aukštesniu tikslumu.

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