the aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. the method is a combination of the asymptotic expansion technique and the reproducing kernel method (rkm). first an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. then the reduced regular delayed diffe...

The aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. The method is a combination of the asymptotic expansion technique and the reproducing kernel method (RKM). First an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. Then the reduced regular delayed diffe...

1 Department of Mathematics, Faculty of Science, University of Žilina, Univerzitná 8215/1, 01026 Žilina, Slovakia 2 Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkovskaya Str. 3, 01601 Kyiv, Ukraine 3 Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, Veveřı́ 331/95, 60200 Brno, Czech Republic 4 Departme...

In this paper, the boundary value problems for second order singularly perturbed delay differential equations are treated. A generic numerical approach based on finite difference is presented to solve such boundary value problems. The stability and convergence analysis of the method is studied. The solution of the boundary value problems when delay is zero, exhibits layer behavior. Here, the st...

by using the trigonometric uniform splines of order 3 with a real tension factor, a numericalmethod is developed for solving a linear second order boundary value problems (2vbp) withdirichlet, neumann and cauchy types boundary conditions. the moment at the knots isapproximated by central finite-difference method. the order of convergence of the methodand the theory is illustrated by solving tes...