An efficient method for solving difference systems for elliptic differential equations

A. A. Abramov^a, L. F. Yukhno<sup>b

a</sup> Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333 Russia
^b Institute of Mathematical Modeling, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047 Russia

Abstract: A method for solving systems of linear algebraic equations arising in connection with the approximation of boundary value problems for elliptic partial differential equations is proposed. This method belongs to the class of conjugate directions method applied to a preliminary transformed system of equations. A model example is used to explain the idea underlying this method and to investigate it. Results of numerical experiments that confirm the method’s efficiency are discussed.

Key words: system of linear algebraic equations, elliptic partial differential equation, conjugate directions method, Craig’s method.

UDC: 519.632.4

Received: 12.04.2011

 English version: Computational Mathematics and Mathematical Physics, 2011, 51:12, 2115–2120

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