Methods for Solving Stationary Problems of Mathematical Physics

1975 ◽  
pp. 87-141
Author(s):  
G. I. Marchuk
2008 ◽  
Vol 13 (3) ◽  
pp. 313-326
Author(s):  
Natali G. Abrashina-Zhadaeva ◽  
Alexey A. Egorov

Additive iterative methods of complete approximation for stationary problems of mathematical physics are proposed. The convergence rate in the case of an arbitrary number of commutative and noncommutative partition operators is analysed. The optimal values of the iterative parameter are found and related estimates for the number of iterations are derived. Some applications of suggested iterative methods are discussed.


Author(s):  
Gennady Shvachych ◽  
Marina Sazonova ◽  
Olena Ivaschenko ◽  
Larysa Sushko

This paper purpose is to construct maximally parallel algorithms for solving economy problems that are described by dynamic models. The problems of mathematical modeling of a similar class of problems on parallel cluster-type computing systems are considered. Most conventional algorithms for solving such problems (methods of runs, decomposition of a matrix into two diagonal matrices, doubling, etc.), with several processors, usually work no faster than with a single processor. This is caused by significant computations’ sequence of such algorithms. The developed procedure of numerical and analytical sampling is quite simply generalized to other types of differential equations of mathematical physics. In particular, in stationary problems it is easier to localize features and apply high-order schemes in the smoothness areas.


Author(s):  
Alexandru Kristaly ◽  
Vicentiu D. Radulescu ◽  
Csaba Varga

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