Results 61 to 70 of about 225 (176)
Journal of Mathematics, Volume 2025, Issue 1, 2025.This paper provides numerical solutions to a class of singularly perturbed differential–difference equations characterized by mixed shift parameters. The solutions of such problems exhibit sharp boundary layers near the endpoints of the spatial domain due to the presence of a small perturbation parameter ε(0 < ε ≪ 1).
Amare Worku Demsie +3 more
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Some uniformly convergent schemes on Shishkin mesh
Novi Sad Journal of Mathematics - NSJOM, 1998 Given the selfadjoint problem \[ \begin{gathered} Ly\equiv-\varepsilon y''+p(x)y=f(x),\quad x\in I=(0,1)\\ y(0)=0,\quad y(1))=0 \end{gathered} \] where \(00\), a difference scheme on the non-uniform mesh was derived by the use of cubic spline. The proposed scheme is analyzed and proved to be uniformly convergent with the order \(O(n^{-2}\ln^2n)\).
Vukoslavčević, Vanja +2 more
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Fitted Numerical Scheme for Singularly Perturbed Convection‐Diffusion Equation with Small Time Delay
International Journal of Mathematics and Mathematical Sciences, Volume 2024, Issue 1, 2024.In this article, a uniformly convergent numerical scheme is developed to solve a singularly perturbed convection‐diffusion equation with a small delay having a boundary layer along the left side. A priori bounds of continuous solution and its derivatives are discussed.
Sisay Ketema Tesfaye +4 more
wiley +1 more source
A robust computational technique for a system of singularly perturbed reaction–diffusion equations
International Journal of Applied Mathematics and Computer Science, 2014 In this paper, a singularly perturbed system of reaction–diffusion Boundary Value Problems (BVPs) is examined. To solve such a type of problems, a Modified Initial Value Technique (MIVT) is proposed on an appropriate piecewise uniform Shishkin mesh.
Kumar Vinod +2 more
doaj +1 more source
A new second-order difference approximation for nonlocal boundary value problem with boundary layers
Mathematical Modelling and Analysis, 2020 The aim of this paper is to present finite difference method for numerical solution of singularly perturbed linear differential equation with nonlocal boundary condition.
Derya Arslan
doaj +1 more source
Computational and Mathematical Methods, Volume 2024, Issue 1, 2024.In this study, we consider a parameter‐uniform convergent numerical approach for a class of time‐fractional singularly perturbed partial differential equations (TF‐SPDPDEs) with large delay in time that exhibits a regular exponential boundary layer on the right side of the spatial domain.
Habtamu Getachew Kumie +3 more
wiley +1 more source
Fitted Tension Spline Scheme for a Singularly Perturbed Parabolic Problem With Time Delay
Journal of Applied Mathematics, Volume 2024, Issue 1, 2024.A fitted tension spline numerical scheme for a singularly perturbed parabolic problem (SPPP) with time delay is proposed. The presence of a small parameter ε as a multiple of the diffusion term leads to the suddenly changing behaviors of the solution in the boundary layer region.
Sisay Ketema Tesfaye +4 more
wiley +1 more source
Indoor Air, Volume 2024, Issue 1, 2024.Current models to determine the risk of airborne disease infection are typically based on a backward quantification of observed infections, leading to uncertainties, e.g., due to the lack of knowledge whether the index person was a superspreader. In contrast, the present work presents a forward infection risk model that calculates the inhaled dose of ...
Florian Webner +4 more
wiley +1 more source
Mathematical Modelling and Analysis, 2018 In this paper, an adaptive mesh strategy is presented for solving singularly perturbed delay differential equation of convection-diffusion type using second order central finite difference scheme.
Pramod P. Chakravarthy +2 more
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Advances in Mathematical Physics, Volume 2024, Issue 1, 2024.In this paper, a numerical scheme for a time‐dependent singularly perturbed parabolic convection–diffusion problem with boundary turning points is presented. The problem exhibits a left boundary layer in the spatial domain. We use the Crank–Nicolson method for temporal discretization and a nonstandard finite difference approach for spatial ...
Yimesgen Mehari Kebede +3 more
wiley +1 more source