<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this study we investigated the singularly perturbed boundary value problems for semilinear reaction-difussion equations. We have introduced a basic and computational approach scheme based on Numerov’s type on uniform mesh. We indicated that the method is uniformly convergence, according to the discrete maximum norm, independently of the parameter of <italic>ɛ</italic>. The proposed method was supported by numerical example.</p></abstract>

In this study we investigated the singularly perturbed boundary value problems for semilinear reaction-difussion equations. We have introduced a basic and computational approach scheme based on Numerov’s type on uniform mesh. We indicated that the method is uniformly convergence, according to the discrete maximum norm, independently of the parameter of ɛ. The proposed method was supported by numerical example.

A Numerical Scheme For Semilinear Singularly Perturbed Reaction-Diffusion Problems

Dep. of Mathematics and Science Education

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

In this study we investigated the singularly perturbed boundary value problems for semilinear reaction-difussion equations. We have introduced a basic and...

ɛ	N = 32	N = 64	N = 128	N = 256	N = 512	$R_{ε}^{N}$ R_\varepsilon ^N
2⁻⁵	2.3e–4	5.9e–5	1.5e–5	3.7e–6	9.2e–7	2.009
2⁻⁶	3.8e–4	9.5e–5	2.4e–5	6.2e–6	1.5e–6	2.014
2⁻⁷	6.4e–4	1.6e–4	4.0e–5	1.0e–5	2.5e–6	2.019
2⁻⁸	1.1e–3	2.4e–4	6.9e–5	1.7e–5	4.3e–6	2.020
2⁻⁹	1.9e–3	4.9e–4	1.2e–4	3.1e–5	7.6e–6	2.015
R^N	2.013	2.003	2.002	1.998	2.020

A Numerical Scheme For Semilinear Singularly Perturbed Reaction-Diffusion Problems

Published Online: Mar 31, 2020

Page range: 405 - 412

Received: Jun 06, 2019

Accepted: Aug 05, 2019

DOI: https://doi.org/10.2478/amns.2020.1.00038

Keywords
Singular perturbations, reaction-diffusion problems, numerov method

© 2019 Kerem Yamac et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Maximum errors and rates of convergence wh

A Numerical Scheme For Semilinear Singularly Perturbed Reaction-Diffusion Problems

Published Online: Mar 31, 2020

Page range: 405 - 412

Received: Jun 06, 2019

Accepted: Aug 05, 2019

DOI: https://doi.org/10.2478/amns.2020.1.00038

KeywordsSingular perturbations, reaction-diffusion problems, numerov method

© 2019 Kerem Yamac et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Maximum errors and rates of convergence wh

Keywords
Singular perturbations, reaction-diffusion problems, numerov method