A semilinear reaction-diffusion two-point boundary value problem, whose secondorder derivative is multiplied by a small positive parameter ε2, is considered. It can have multiple solutions. The numerical computation of solutions having interior transition layers is analysed. It is demonstrated that the accurate computation of such solutions is exceptionally difficult. To address this difficulty...

ABSTRACT. In this paper, a numerical method is constructed for solving one-dimensional time dependent modified Burgers’ equation for various values of Reynolds number. At high Reynolds number, an inviscid boundary layer is produced in the neighborhood of right part of the lateral surface of the domain and the problem can be considered as a non-linear singularly perturbed problem involving a sma...

In the present paper we consider a boundary value problem on the semiaxis (0;∞) for a singularly perturbed parabolic equation with the two perturbation parameters 1 and 2 multiplying, respectively, the second and 5rst derivatives with respect to the space variable. Depending on the relation between the parameters, the di7erential equation can be either of reaction–di7usion type or of convection...

Consider the singularly perturbed linear reaction-diffusion problem −ε2Δu+ bu = f in Ω ⊂ Rd, u = 0 on ∂Ω, where d ≥ 1, the domain Ω is bounded with (when d ≥ 2) Lipschitzcontinuous boundary ∂Ω, and the parameter ε satisfies 0 < ε 1. It is argued that for this type of problem, the standard energy norm v → [ε|v|1+‖v‖0] is too weak a norm to measure adequately the errors in solutions computed by f...

The article is devoted to the comparative analysis of organisation spatio-temporal structures in novel “Ulysses” by James Augustine Aloysius Joyce and literary-historical guide “Russian Switzerland” Mikhail Shishkin. general way permeability boundaries fiction – non-fiction genres reflection this process world Russian literature 20th–21st centuries investigated. It proved that for Shishkin, as ...

This article presents a study on singularly perturbed 1D parabolic Dirichlet’s type differential equations with discontinuous source terms an interior line. The time derivative is discretized using the Euler backward method, followed by application of streamline–diffusion finite element method (SDFEM) to solve locally one-dimensional stationary problems Shishkin mesh. Our proposed shown achieve...

objectives: indicators of oral health-related quality of life (ohrqol) in children are widely adopted to evaluate the effects of oral problems. recently, the scale of oral health outcomes for 5-year-old children (soho-5) was developed based on the children’s self-reports. this study aimed to evaluate the validity and reliability of the persian version of the questionnaire in a sample of iranian...

In this article, a numerical solution is proposed for singularly perturbed delay parabolic reaction-diffusion problem with mixed-type boundary conditions. The discretized by the implicit Euler method on uniform mesh in time and extended cubic B-spline collocation Shishkin space. parameter-uniform convergence of given, it shown to be ...