Mustafa Kudu

Uniform difference method for a parameterized singular perturbation problem

We consider a uniform finite difference method on a B-mesh is applied to solve a singularly perturbed quasilinear boundary value problem (BVP) depending on a parameter. We give a uniform first-order error estimates in a discrete maximum norm. Numerical results are presented that demonstrate the sharpness of our theoretical analysis.

A numerical treatment for singularly perturbed differential equations with integral boundary condition

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.

Finite-difference method for parameterized singularly perturbed problem

We study uniform finite-difference method for solving first-order singularly perturbed boundary value problem (BVP) depending on a parameter. Uniform error estimates in the discrete maximum norm are obtained for the numerical solution. Numerical results support the theoretical analysis.

A finite-difference method for a singularly perturbed delay integro-differential equation

We consider the singularly perturbed initial value problem for a linear first order Volterra integro-differential equation with delay. Our purpose is to construct and analyse a numerical method with uniform convergence in the perturbation parameter. The numerical solution of this problem is discretized using implicit difference rules for differential part and the composite numerical quadrature rules for integral part. On a layer-adapted mesh error estimations for the approximate solution are established. Numerical examples supporting the theory are presented.

Analysis of the Layer Behavior to the Parameterized Problem with Integral Boundary Condition

Bu calismada, integral sinir sartli parametreye bagli singuler perturbe ozellikli kuazi-lineer sinir-deger problemi ele alinmistir. Problemin cozumu ve birinci turevleri icin asimptotik degerlendirmeler elde edilmistir. Bu teorik sonuclari destekleyen ve degerlendirmelerin kesin oldugunu gosteren bir ornek verilmistir. Asimptotik degerlendirmelerin elde edilmesinde kullanilan yontem uygun numerik cozumlerin incelenmesinde kullanilabilir.

Analysis of Difference Approximations to Delay Pseudo-Parabolic Equations

This work deals with the one-dimensional initial-boundary Sobolev or pseudo-parabolic problem with delay. For solving this problem numerically, we construct fourth-order difference-differential scheme and obtain the error estimate for its solution. Further, for the time variable, we use the appropriate Runge–Kutta method for the realization of our differential-difference problem. Numerical results supporting the theory are presented.