Geodesic
Iterative factorization on fictitious continuation for the numerical solution of elliptic equation of the fourth order
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 6 (2014) no. 2, pp. 17-22

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The elliptic differential equation of the fourth order is considered under the mixed boundary conditions. The numerical solution is reduced to the solution of the system of linear algebraic equations with triangular matrices, in which quantity of nonzero elements in every line is less than three, by means of iterative factorization on fictitious continuation.
Keywords: iterative factorization, fictitious continuation. 
A. L. Ushakov. Iterative factorization on fictitious continuation for the numerical solution of elliptic equation of the fourth order. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 6 (2014) no. 2, pp. 17-22. http://geodesic.mathdoc.fr/item/VYURM_2014_6_2_a2/
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[4] Ushakov A. L., An approximate solution of elliptic boundary value problem of fourth order, Chelyabinskiy gosudarstvennyy tekhnicheskiy universitet Publ., Chelyabinsk, 1997, 30 pp. (in Russ.)