a hybrid method for singularly perturbed delay boundary value problems exhibiting a right boundary layer
Authors
abstract
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 differential equation is solved analytically using the rkm. an error estimate and two numerical examples are provided to illustrate the effectiveness of the present method. the results of numerical examples show that the present method is accurate and efficient.
similar resources
A hybrid method for singularly perturbed delay boundary value problems exhibiting a right boundary layer
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...
full textA New Method for Solving Singularly Perturbed Boundary Value Problems
In this paper, a new initial value method for solving a class of nonlinear singularly perturbed boundary value problems with a boundary layer at one end is proposed. The method is designed for the practicing engineer or applied mathematician who needs a practical tool for these problems (easy to use, modest problem preparation and ready computer implementation). Using singular perturbation anal...
full textShooting Method for Nonlinear Singularly Perturbed Boundary-value Problems
Asymptotic formulas, as ε → 0, are derived for the solutions of the nonlinear differential equation εu+Q(u) = 0 with boundary conditions u(−1) = u(1) = 0 or u′(−1) = u(1) = 0. The nonlinear term Q(u) behaves like a cubic; it vanishes at s−, 0, s+ and nowhere else in [s−, s+], where s− < 0 < s+. Furthermore, Q (s±) < 0, Q (0) > 0 and the integral of Q on the interval [s−, s+] is zero. Solutions ...
full textFitted mesh numerical method for singularly perturbed delay differential turning point problems exhibiting boundary layers
Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opin...
full textHigh-order Methods for Semilinear Singularly Perturbed Boundary Value Problems
We considered finite difference methods of higher order for semilinear singularly perturbed boundary value problems, consisted of constructing difference schemes on nonuniform meshes. Construction of schemes is presented and convergence uniform in perturbation parameter for one method is shown on Bakhvalov’s type of mesh. Numerical experiments demonstrated influence of different meshes on devel...
full textRobust Monotone Iterates for Nonlinear Singularly Perturbed Boundary Value Problems
Recommended by Donal O'Regan This paper is concerned with solving nonlinear singularly perturbed boundary value problems. Robust monotone iterates for solving nonlinear difference scheme are constructed. Uniform convergence of the monotone methods is investigated, and convergence rates are estimated. Numerical experiments complement the theoretical results.
full textMy Resources
Save resource for easier access later
Journal title:
bulletin of the iranian mathematical societyPublisher: iranian mathematical society (ims)
ISSN 1017-060X
volume 41
issue 5 2015
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023