Results 41 to 50 of about 225 (176)

Spline‐Based Computational Technique for Singularly Perturbed Fredholm Integro‐Differential Problems

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
In this work, using a spline‐based discretization, we develop a computational approach for singularly perturbed Fredholm integro‐differential equations. The scheme addresses the challenges of the singular perturbation parameter ϵ through a tension and compression spline technique, coupled with Simpson’s rule for quadrature approximations.
Rajagopal S., Dinesh Kumar S., Patricia J. Y. Wong   +2 more
wiley   +1 more source

Advanced Fitted Mesh Finite Difference Strategies for Solving ‘n’ Two-Parameter Singularly Perturbed Convection–Diffusion System

Axioms
This paper proposes a robust finite difference method on a fitted Shishkin mesh to solve a system of n singularly perturbed convection–reaction–diffusion differential equations with two small parameters.
Jenolin Arthur, Joseph Paramasivam Mathiyazhagan, George E. Chatzarakis, S. L. Panetsos   +3 more
doaj   +1 more source

Some numerical experiments with multigrid methods on Shishkin meshes

Journal of Computational and Applied Mathematics, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gaspar, F.J., Clavero, C., Lisbona, F.
openaire   +2 more sources

A Hybrid Computational Approach for Singularly Perturbed Parabolic Differential Equations Involving Small Negative Shift Parameters

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
The present paper addresses the numerical computation of singularly perturbed differential equations incorporating small negative shift parameters in the convection and reaction terms. Since the diffusion term is scaled by a sufficiently small parameter ε(0 < ε ≪ 1), the solution typically develops multiscale characteristics manifested through boundary
Amare Worku Demsie, Awoke Andargie Tiruneh, Endalew Getnet Tsega, Shikha Binwal   +3 more
wiley   +1 more source

A Hybrid Fitted Mesh Numerical Scheme for Solving Singularly Perturbed Reaction–Diffusion Equation With Mixed Shifts

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This study develops a robust hybrid numerical scheme for a class of time‐dependent, singularly perturbed differential‐difference equations characterized by a small positive parameter multiplying the highest order derivative term and mixed spatial shifts (delay and advance) in the reaction terms.
Ababi H. Ejere, Gemechis F. Duressa, Mesfin M. Woldaregay, Tekle G. Dinka, Smritijit Sen   +4 more
wiley   +1 more source

A Parameter Uniform Almost First Order Convergent Numerical Method for a Semi-Linear System of Singularly Perturbed Delay Differential Equations

Biomath, 2014
In this paper an initial value problem for asemi-linear system of two singularly perturbed first order delay differential equations is considered on the interval(0,2]. The components of the solution of this system exhibit initial layers at 0 and interior
Nagaranjan Shivaranjan, John J H Miller, Sigmani Valarmathi   +2 more
doaj   +3 more sources

A novel hybrid numerical method for delay differential equations with delay-dependent nonlocal condition

Arab Journal of Basic and Applied Sciences
This paper develops a novel hybrid numerical method for the [Formula: see text]-uniform approximation of singularly perturbed second-order delay differential equations subject to delay-dependent nonlocal boundary condition.
Zelal Temel
doaj   +1 more source

A Quintic Spline-Based Computational Method for Solving Singularly Perturbed Periodic Boundary Value Problems

Axioms
This work aims to provide approximate solutions for singularly perturbed problems with periodic boundary conditions using quintic B-splines and collocation. The well-known Shishkin mesh strategy is applied for mesh construction.
Puvaneswari Arumugam, Valanarasu Thynesh, Chandru Muthusamy, Higinio Ramos   +3 more
doaj   +1 more source

Accelerated Fitted Mesh Scheme for Singularly Perturbed Turning Point Boundary Value Problems

Journal of Mathematics, 2022
An accelerated fitted mesh scheme is proposed for the numerical solution of the singularly perturbed boundary value problems whose solution exhibits an interior layer near the turning point.
Tesfaye Aga Bullo
doaj   +1 more source

A Robust Exponentially Fitted Scheme for Singularly Perturbed Fractional‐Order Delay Parabolic Equation

Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.
This study introduces a fitted numerical approach for solving singularly perturbed time‐fractional parabolic differential equations incorporating a delay term. The stability of the method is rigorously examined using the comparison principle and solution bounds, while its convergence is analyzed through the barrier function approach and the Peano ...
Nuru Ahmed Endrie, Gemechis File Duressa, Mohammad Mirzazadeh   +2 more
wiley   +1 more source