Samir Karasuljic

University of Tuzla | UNTZ · Department of Mathematics

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...

This paper describes new forms of layer-damping functions eliminating singularities of solutions to singularly-perturbed problems and corresponding layer-resolving grids

This paper demonstrates results of numerical experiments on some popular and new layer-resolving grids applied for solving one-dimensional singularly-perturbed problems having power of the first type boundary layers. В статье приведены результаты численных расчетов обыкновенных сингулярно-возмущенных задач, решения которых имеют степенные, первого...

The paper describes an explicit approach for generating layer–resolving grids in problems having exponential or power–of–first–type layers. The grids are generated on the basis of qualitative estimates of solution derivatives in the layers of one-dimensional singularly perturbed problems. The paper presents results of numerical experiments, using a...

In the 50 years since Bakhvalov published his paper , the conversation within the SPP community has centered largely on problems with exponential layers. Such layers mainly occur in problems for which the solutions of reduced (ε = 0) problems do not have singularities. The layer-damping coordinate mappings described in this book for non-exponential...

In the present paper we consider the numerical solving of a semilinear singular--perturbation reaction--diffusion boundary--value problem having boundary layers. A new difference scheme is constructed, the second order of convergence on a modified Shishkin mesh is shown. The numerical experiments are included in the paper, which confirm the theoret...

The book was written on the basis of materials that we presented at several faculties, either as lectures or as part of auditory exercises. Aware that there are more books and textbooks in the area in which the topics covered by this book are covered, we tried, based on the mentioned experience, to write a book oriented towards students.

A class of different schemes for finding the numerical solution of semilinear singularly--perturbed reaction--diffusion boundary--value problems was constructed. The stability of the difference schemes was proved, and the existence and uniqueness of a numerical solution were shown. After that, the uniform convergence with respect to a perturbation...

A class of different schemes for the numerical solving of semilinear singularly--perturbed reaction--diffusion boundary--value problems was constructed. The stability of the difference schemes was proved, and the existence and uniqueness of a numerical solution were shown. After that, the uniform convergence with respect to a perturbation parameter...

In this paper we consider two difference schemes for numerical solving of a one-dimensional singularly perturbed boundary value problem. We proved an ε-uniform convergence for both difference schemes on a Shishkin mesh. Finally, we present four numerical experiments to confirm the theoretical results.

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 $\varepsilon$-uniform convergence of such gained the ap...

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...