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Uniform finite difference methods are constructed via nonstandard finite difference methods for the numerical solution of singularly perturbed quasilinear initial value problem for delay differential equations. A numerical method is constructed for this problem which involves the appropriate Bakhvalov meshes on each time subinterval. The method is shown to… (More)

- Gabil M. Amiraliyev, Fevzi Erdogan
- Computers & Mathematics with Applications
- 2007

- Mehmet Giyas Sakar, Fevzi Erdogan, Ahmet Yildirim
- Computers & Mathematics with Applications
- 2012

- I. G. Amiraliyeva, Fevzi Erdogan, Gabil M. Amiraliyev
- Appl. Math. Lett.
- 2010

This paper deals with singularly perturbed initial value problem for linear first-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. The difference scheme is shown to be uniformly convergent to the continuous solution… (More)

- Gabil M. Amiraliyev, Fevzi Erdogan
- Numerical Algorithms
- 2009

This study deals with the singularly perturbed initial value problem for a quasilinear first-order delay differential equation. A numerical method is generated on a grid that is constructed adaptively from a knowledge of the exact solution, which involves appropriate piecewise-uniform mesh on each time subinterval. An error analysis shows that the method is… (More)

- Zhongdi Cen, Fevzi Erdogan, Aimin Xu
- Numerical Algorithms
- 2013

In this paper a nonlinear singularly perturbed initial problem is considered. The behavior of the exact solution and its derivatives is analyzed, and this leads to the construction of a Shishkin-type mesh. On this mesh a hybrid difference scheme is proposed, which is a combination of the second order difference schemes on the fine mesh and the midpoint… (More)

- Fevzi Erdogan, Gabil M. Amiraliyev
- Numerical Algorithms
- 2011

This paper deals with singularly perturbed initial value problem for 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. The difference scheme is shown to be uniformly convergent to the continuous solution… (More)

- Fevzi Erdogan
- 2008

In this paper a certain class of singular integral equations that may arise from the mixed boundary value problems in nonhomogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral… (More)

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