The figures and the tables show this competence and low errors.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, the system of singularly Perturbed Reaction-Diffusion problems which are commonly used in physics and chemistry branches of science, were investigated.
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Key Findings & Data:Sinc-Galerkin Method was used to obtaining the solution of problems.
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Conclusion & Impact:The figures and the tables show this competence and low errors.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Sinc-Galerkin method · system of singularly perturbed reaction-diffusion problems · Perturbed Reaction-Diffusion problems
Abstract
In this paper, the system of singularly Perturbed Reaction-Diffusion problems which are commonly used in physics and chemistry branches of science, were investigated. Sinc-Galerkin Method was used to obtaining the solution of problems. Because of there is no article about Sinc-Galerkin Method related to singularly perturbed Reaction-Diffusion problems in literature, the efficiency of the method was shown via this problem. There are important results that occurred after our research and application. Sinc Galerkin Method which was used in this paper as the main solution method gave better results according to parameter robust method and asymptotical initial value method. The figures and the tables show this competence and low errors.
SECER, A., ONDER, I., OZISIK, M. (2021). Sinc-Galerkin method for solving system of singular perturbed reaction-diffusion problems. Sigma Mühendislik ve Fen Bilimleri Dergisi, Cilt: 39 - Sayı: 2, 203–212. https://ajindex.com/articles/419029
Kumar M, Parul. Methods for solving singular perturbation problems arising in science and engineering. Math Comput Model 2011
Li G, Luo P, Peng S, Wang C, Xiang CL. A singularly perturbed Kirchhoff problem revisited. J Differ Equ 2020;268:541–89
Zhumanazarova A, Cho YI. Asymptotic Convergence of the Solution of a Singularly Perturbed Integro-Differential Boundary Value Problem. Mathematics 2020;8:213
Geng FZ. Piecewise reproducing kernel-based symmetric collocation approach for linear stationary singularly perturbed problems n.d
Kumar S, Kumar S. High‐order convergent methods for singularly perturbed quasilinear problems with integral boundary conditions. Math Methods Appl Sci 2020:mma.6854
Matthews S, O’Riordan E, Shishkin GI. A numerical method for a system of singularly perturbed reaction-diffusion equations. J Comput Appl Math 2002
Linß T, Madden N. A finite element analysis of a coupled system of singularly perturbed reaction-diffusion equations. Appl Math Comput 2004
Lin R, Stynes M. A balanced finite element method for a system of singularly perturbed reaction-diffusion two-point boundary value problems. Numer Algorithms 2015
Cai Z, Ku J. A dual finite element method for a singularly perturbed reaction-diffusion problem. SIAM J Numer Anal 2020;58:1654–73
Linss T. Analysis of a System of Singularly Perturbed Convection-Diffusion Equations with Strong Coupling. SIAM J Numer Anal 2009
Bellew S, O’Riordan E. A parameter robust numerical method for a system of two singularly perturbed convection-diffusion equations. Appl Numer Math 2004
Mustafa G, Ejaz ST, Baleanu D, Ghaffar A, Nisar KS. A subdivision-based approach for singularly perturbed boundary value problem. Adv Differ Equations 2020;2020:282
Cen Z, Liu L Bin, Xu A. A second-order adaptive grid method for a nonlinear singularly perturbed problem with an integral boundary condition. J Comput Appl Math 2021;385:113205
El-Gamel M, Cannon JR. On the solution a of second order singularly-perturbed boundary value problem by the Sinc-Galerkin method. Zeitschrift Fur Angew Math Und Phys 2005
Stenger F. A “Sinc-Galerkin” Method of Solution of Boundary Value Problems. Math Comput 1979
Secer A, Kurulay M. The sinc-Galerkin method and its applications on singular Dirichlet-type boundary value problems. Bound Value Probl 2012
Secer A, Kurulay M, Bayram M, Akinlar MA. An efficient computer application of the sinc-Galerkin