Browsing by Author "Amiraliyeva, I. G."

Now showing 1 - 4 of 4

Difference Schemes for the Singularly Perturbed Sobolev Equations
(World Scientific Publ Co Pte Ltd, 2007) Amiraliyev, G. M.; Amiraliyeva, I. G.
The present study is concerned with the numerical solution, using finite difference method of a one-dimensional initial-boundary value problem for a quasilinear Sobolev or pseudo-parabolic equation with initial jump. We have derived a method based on using finite elements with piecewise linear functions in space and with exponential functions in time and appropriate quadrature formulae with remainder term in integral form. In the initial layer, we introduce a special non-uniform mesh which is constructed by using estimates of derivatives of the exact solution and the analysis of the local truncation error. For the time integration we use the implicit rule. The fully discrete scheme is shown to be convergent of order 2 in space and of order one in time, uniformly in the singular perturbation parameter. Numerical results supporting the theory are presented.
A Numerical Treatment for Singularly Perturbed Differential Equations With Integral Boundary Condition
(Elsevier Science inc, 2007) Amiraliyev, G. M.; Amiraliyeva, I. G.; Kudu, Mustafa
We consider a uniform finite difference method on Shishkin mesh for a quasilinear first order singularly perturbed boundary value problem (BVP) with integral boundary condition. We prove that the method is first order convergent except for a logarithmic factor, in the discrete maximum norm, independently of the perturbation parameter. The parameter uniform convergence is confirmed by numerical computations. (c) 2006 Elsevier Inc. All rights reserved.
A Parameter-Uniform Numerical Method for a Sobolev Problem With Initial Layer
(Springer, 2007) Amiraliyev, G. M.; Duru, Hakki; Amiraliyeva, I. G.
The present study is concerned with the numerical solution, using finite difference method of a one-dimensional initial-boundary value problem for a linear Sobolev or pseudo-parabolic equation with initial jump. In order to obtain an efficient method, to provide good approximations with independence of the perturbation parameter, we have developed a numerical method which combines a finite difference spatial discretization on uniform mesh and the implicit rule on Shishkin mesh(S-mesh) for the time variable. The fully discrete scheme is shown to be convergent of order two in space and of order one expect for a logarithmic factor in time, uniformly in the singular perturbation parameter. Some numerical results confirming the expected behavior of the method are shown.
A Uniform Numerical Method for Dealing With a Singularly Perturbed Delay Initial Value Problem
(Pergamon-elsevier Science Ltd, 2010) Amiraliyeva, I. G.; Erdogan, F.; Amiraliyev, G. M.
This work deals with a singularly perturbed initial value problem fora quasi-linear second-order delay differential equation. An exponentially fitted difference scheme is constructed, in an equidistant mesh, which gives first-order uniform convergence in the discrete maximum norm. Numerical results are also presented. (C) 2010 Elsevier Ltd. All rights reserved.