Enes Duvnjaković- PhD
- Professor (Full) at University of Tuzla
Enes Duvnjaković
- PhD
- Professor (Full) at University of Tuzla
About
21
Publications
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78
Citations
Introduction
Nonlinear singularly-perturbed boundary problems
Current institution
Publications
Publications (21)
In this paper we consider the semilinear singularly perturbed reaction--diffusion boundary value problem. In the first part of the paper a difference scheme is given for the considered problem. In the main part of the paper a cubic spline is constructed and we show that it represents a global approximate solution of the our problem. At the end of t...
The textbook "Metric spaces" was written and accepted for use as a university textbook at the University of Tuzla. It is written in Bosnian and intended for native Bosnian speakers, as is the description below. CIP - Katalogizacija u publikaciji Nacionalna i univerzitetska biblioteka Bosne i Hercegovine, Sarajevo 515.124(075.8)
Iako možda svako od...
In this paper we consider the numerical solution of a singularly perturbed one-dimensional semilinear reaction-diffusion problem. We construct a class of finite-difference schemes to discretize the problem and we prove that the discrete system has a unique solution. The central result of the paper is second-order convergence uniform in the perturba...
In this paper we consider the numerical solution of a singularly perturbed one-dimensional semilinear reaction-diffusion problem. A class of differential schemes is constructed. There is a proof of the existence and uniqueness of the numerical solution for this constructed class of differential schemes. The central result of the paper is an $\varep...
In this paper we consider two difference schemes for numerical solving of a one--dimensional singularly perturbed boundary value problem. We proved an $\varepsilon$--uniform convergence for both difference schemes on a Shiskin mesh. Finally, we present four numerical experiments to confirm the theoretical results.
We consider an approximate solution for the one–dimensional semilinear singularly–perturbed boundary value problem, using the previously obtained numerical values of the boundary value problem in the mesh points and the representation of the exact solution using Green’s function. We present an "epsilon–uniform convergence of such gained the approxi...
We consider an approximate solution for the one-dimensional semilinear singularly-perturbed boundary value problem, using the previously obtained numerical values of the boundary value problem in the mesh points and the representation of the exact solution using Green's function. We present an $\varepsilon$-uniform convergence of such gained the ap...
We consider an approximate solution for the one-dimensional semilinear singularly-perturbed boundary value problem, using the previously obtained numerical values of the boundary value problem in the mesh points and the representation of the exact solution using Green's function. We present an $\varepsilon$-uniform convergence of such gained the ap...
For singularly perturbed selfadjoint one-dimensional reaction-di¤usion problem, using the Galerkin
method with exponential test function, a class of di¤erence schemes is given, which is second-order
accurate at nodes uniformly in the parameter. A numerical example is included.
We consider Banach sequence spaces lp;� with a weighted sequence �,
which are generalizations of standard sequence spaces. We investigate the relationships
between these spaces for a xed p (1 � p � +1) and for di�erent weighted
functions, as well as for xed � and various p; q (1 � p < q � +1). We also present
the representation of bounded linear fu...
In this work we consider the singularly perturbed one-dimensional semi-linear reaction-diffusion problem " y (x) = f (x; y); x 2 (0; 1) ; y(0) = 0; y(1) = 0; where f is a nonlinear function. Here the second-order derivative is multiplied by a small positive parameter and consequently, the solution of the problem has boundary layers. A new differenc...
In this paper we are considering a semilinear singular perturbation reaction
-- diffusion boundary value problem, which contains a small perturbation
parameter that acts on the highest order derivative. We construct a difference
scheme on an arbitrary nonequidistant mesh using a collocation method and
Green's function. We show that the constructed...
The paper examines a semilinear singular reaction-diffusion problem. Using the col-
location method with naturally chosen splines of exponential type, a new difference scheme on a mesh of Bakhvalov type is constructed. A difference scheme generates the system of non-linear equations, and the theorem of existence and this system’s solution uniquenes...
We consider the singularly perturbed selfadjoint one-dimensional semilinear reaction-diffusion problem () () 2 : , L y y x f x y ε ε ′′ = = , on () 1 , 0 () 0 0 = y ; () 0 1 = y , where f(x,y) is a non-linear function. For this problem, using the spline-method with the natural choice of functions, a new difference scheme is given on a non-uniform m...
In this paper we consider semilinear elliptic Dirichlets boundary value problem with small parameter, well known as singularly perturbed semilinear reaction-diffusion problem. Using theory of projection-mesh methods, precisely using the Galerkin method with natural choice of test function, the given boundary problem is discretized and we get a disc...
For singularly perturbed selfadjoint one-dimensional reaction-diffusion problems, using the Galerkin method with an exponential test function, a class of difference schemes is given, which is second-order accurate at nodes for the fixed perturbation parameter. A numerical example is included.
