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- Rakhim Aitbayev, Bernard Bialecki
- SIAM J. Numerical Analysis
- 2003

We study the computation of the orthogonal spline collocation solution of a linear Dirichlet boundary value problem with a nonselfadjoint or an indefinite operator of the form Lu = a ij (x)ux i x j + b i (x)ux i + c(x)u. We apply a preconditioned conjugate gradient method to the normal system of collocation equations with a preconditioner associated with a… (More)

- Rakhim Aitbayev, Bernard Bialecki
- SIAM J. Numerical Analysis
- 2000

- Rakhim Aitbayev
- 2007

A quadrature Galerkin scheme with the Bogner–Fox–Schmit element for a biharmonic problem on a rectangular polygon is analyzed for existence, uniqueness, and convergence of the discrete solution. It is known that a product Gaussian quadrature with at least three-points is required to guarantee optimal order convergence in Sobolev norms. In this article,… (More)

- Rakhim Aitbayev
- SIAM J. Numerical Analysis
- 2005

Efficient numerical algorithms are developed and analyzed that implement symmetric multilevel preconditioners for the solution of an orthogonal spline collocation (OSC) discretization of a Dirichlet boundary value problem with a non–self-adjoint or an indefinite operator. The OSC solution is sought in the Hermite space of piecewise bicubic polynomials. It… (More)

- Rakhim Aitbayev, Nazgul Yergaliyeva
- Adv. Numerical Analysis
- 2014

A quadrature finite element Galerkin scheme for a Dirichlet boundary value problem for the biharmonic equation is analyzed for a solution existence, uniqueness, and convergence. Conforming finite element space of Bogner-Fox-Schmit rectangles and an integration rule based on the two-point Gaussian quadrature are used to formulate the discrete problem. An H… (More)

- R Aitbayev, X C Cai
- 2004

We discuss our preliminary experiences with several parallel two-level additive S c hwarz type domain decomposition methods for the simulation of three-dimensional transonic compressible ows. The focus is on the implementation of the parallel coarse mesh solver which is used to reduce the computational cost and speed up the convergence of the linear… (More)

- RAKHIM AITBAYEV
- 2013

We obtain sufficient conditions, easily verifiable, for the existence and uniqueness of piecewise smooth solutions of a linear two-point boundary-value problem with general interface conditions. The coefficients of the differential equation may have jump discontinuities at the interface point. As an example, the conditions obtained are applied to a problem… (More)

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