Open AccessSTABILITY ANALYSIS OF SEIDEL TYPE MULTICOMPONENT ITERATIVE METHOD
Author(s) -
V. N. Abrashin,
Raimondas Čiegis,
Violeta Pakenienė,
N. G. Zhadaeva
Publication year - 2002
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2002.9637172
Subject(s) - mathematics , iterative method , stability (learning theory) , convergence (economics) , norm (philosophy) , type (biology) , mathematical analysis , mathematical optimization , computer science , ecology , machine learning , political science , law , economics , biology , economic growth
This paper deals with the stability analysis of multicomponent iterative methods for solving elliptic problems. They are based on a general splitting method, which decomposes a multidimensional parabolic problem into a system of one dimensional implicit problems. Error estimates in the L 2 norm are proved for the first method. For the stability analysis of Seidel type iterative method we use a spectral method. Two dimensional and three dimensional problems are investigated. Finally, we present results of numerical experiments. Our goal is to investigate the dependence of convergence rates of multicomponent iterative methods on the smoothness of the solution. Hence we solve a discrete problem, which approximates the 3D Poisson's problem. It is proved that the number of iterations depends weakly on the number of grid points if the exact solution and the initial approximation are smooth functions, both. The same problem is also solved by the Stability Correction iterative method. The obtained results indicate a similar behavior.