Sahin, Birol; Ashyralyev, A; Malkowsky, E

Two dimensional natural convection heat transfer in a square enclosure is numerically analyzed. Laminar naturalconvection heat transfer is studied by solving the Navier-Stokes and energy equations using finite volume method. Numerical solutions of flow field are obtained by Semi-Implicit Method for Pressure-Linked Equations (SIMPLE). Effects of the discretization schemes on numerical solutions are compared with each other.

Ismailov, Zameddin I.; Cona, Lale; Çevik, Elif Otkun; Guler, Bahadir O.; Ashyralyev, A; Malkowsky, E

In this work, a connection between Weyl numbers of the infinite diagonal matrix with linear bounded operator elements in the direct sum of Banach spaces and its coordinate operators has been investigated.

Ünal, Emrah; Yalçin, Numan; Çelik, Ercan; Ashyralyev, A; Malkowsky, E

In this paper, Hartley series are presented first. Then, the operational matrix of integration together with the product and coefficient matrices are presented. They are used to transform linear differential equation systems to a set of linear algebraic equations. Finally, numerical examples are given.

Ashyralyyev, Charyyar; Cakir, Zafer; Ashyralyev, A; Malkowsky, E

In this paper, some sequences of matrices for matrix pencils are considered. Properties of small singular values of these matrices are investigated. Estimates for singular values are obtained. The result of computer calculations is given.

Ashyralyyev, Charyyar; Cakir, Zafer; Ashyralyev, A; Malkowsky, E

Approximate quadrature formulas for the numerical calculation of the two-dimensional Vekua potential and singular integrals are obtained. The mechanical quadrature method for the two-dimensional quasilinear singular integral equation with Vekua operators is described. The numerical results are compared with the exact solution of the integral equation.

Ashyralyev, Allaberen; Artykov, Merdan; Cakir, Zafer; Ashyralyev, A; Malkowsky, E

In this work, the first and second order of difference schemes that approximately solve the initial-boundary value problem for multidimensional fractional parabolic equation with Dirichlet boundary condition are presented. The stability estimates for the solution of these difference schemes are established.

Ashyralyyev, Charyyar; Dedeturk, Mutlu; Ashyralyev, A; Malkowsky, E

The inverse problem for the multidimensional elliptic equation with Neumann-Dirichlet conditions are presented. For the approximate solution of this inverse problem the first and second order of accuracy in t and in space variables difference schemes are constructed. The stability, almost coercive stability and coercive stability estimates for the solution of these difference schemes are obtained. The algorithm for approximate solution is tested in a two-dimensional inverse problem.

Ashyralyyev, Charyyar; Ashyralyev, A; Malkowsky, E

Inverse problem for an elliptic differential equation with Neumann conditions is considered. Stability and coercive stability estimates for the solution of inverse problem with the overdetermination are obtained. The first and second order of accuracy difference schemes are presented. Stability and coercive stability inequalities for these difference schemes are given. In application, inverse problem for the multidimensional elliptic equation is studied. The first and second order of accuracy difference schemes for the multidimensional inverse problem are presented. Well-posedness of both difference problems are established. The results are supported by a numerical example for the two-dimensional elliptic equation.

Ashyralyyev, Charyyar; Dural, Ayfer; Sozen, Yasar; Ashyralyev, A; Lukashov, A

A finite difference method for the approximate solution of the reverse multidimensional parabolic differential equation with a multipoint boundary condition and Neumann condition is applied. Stability, almost coercive stability, and coercive stability estimates for the solution of the first and second orders of accuracy difference schemes are obtained. The theoretical statements are supported by the numerical example.

Ashyralyev, Allaberen; Emirov, Nazar; Cakir, Zafer; Ashyralyev, A; Lukashov, A

The multidimensional fractional parabolic equation with the Dirichlet-Neumann condition is studied. Stability estimates for the solution of the initial-boundary value problem for this fractional parabolic equation are established. The stable difference schemes for this problem are presented. Stability estimates for the solution of the first order of accuracy difference scheme are obtained. A procedure of modified Gauss elimination method is applied for the solution of first and second order of accuracy difference schemes of one-dimensional fractional parabolic differential equations.