Two illustrative examples are provided to demonstrate the efficiency, robustness, and easy applicabilityof the present method with convergence properties.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:This article focuses on the numerical approximate solution of singularly perturbed systems of secondorderreaction-diffusion two-point boundary-value problems for ordinary differential equations.
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Temel Bulgular & Veri:To handle these typesof problems, a numerical-asymptotic hybrid method has been used.
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Sonuç & Katkı:Two illustrative examples are provided to demonstrate the efficiency, robustness, and easy applicabilityof the present method with convergence properties.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri
Abstract
This article focuses on the numerical approximate solution of singularly perturbed systems of secondorderreaction-diffusion two-point boundary-value problems for ordinary differential equations. To handle these typesof problems, a numerical-asymptotic hybrid method has been used. In this hybrid approach, an efficient asymptoticmethod, the so-called successive complementary expansion method (SCEM) is employed first, and then a numericalmethod based on finite differences is applied to approximate the solution of corresponding singularly perturbed reactiondiffusionsystems. Two illustrative examples are provided to demonstrate the efficiency, robustness, and easy applicabilityof the present method with convergence properties.
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Bu Makaleye Atıf Yap
CENGIZCI, S., NATESAN, S., ATAY, M. T. (2022). An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusion boundary-value problems. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 1, 460–472. https://ajindex.com/articles/607696
Ayaz F. Solutions of the system of differential equations by differential transform method. Appl Math Comput 2004; 147: 547-567
Bellew S, O’Riordan E. A parameter robust numerical method for a system of two singularly perturbed convectiondiffusion equations. Appl Numer Math 2004; 51: 171-186
Biazar J, Babolian E, Islam R. Solution of the system of ordinary differential equations by Adomian decomposition method. Appl Math Comput 2004; 147: 713-719
Cengizci S, Atay MT, Eryilmaz A. A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions. Springerplus 2016; 5: 280
Cengizci S, Eryılmaz A. Successive complementary expansion method for solving Troesch’s problem as a singular perturbation problem. Int J Eng Math 2015; 2015: 949463
Cousteix J, Mauss J. Asymptotic Analysis and Boundary Layers. Scientific Computation, Vol. XVIII. Berlin, Germany: Springer, 2007
Cui M, Geng F. Solving singular two-point boundary value problem in reproducing kernel space. J Comput Appl Math 2007; 205: 6-15
Das, P, Natesan, S. Optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction-diffusion boundary-value problems. Appl Math Comput 2014; 249: 265-277
Farrell PA, Hegarty AF, Miller JJH, O’Riordan E, Shishkin GI. Robust Computational Techniques for Boundary Layers. Boca Raton, FL, USA: Chapman & Hall/CRC, 2000
Gracia JL, Lisbona FJ, O’Riordan E. A coupled system of singularly perturbed parabolic reaction-diffusion equations. Adv Comput Math 2010; 32: 43-61
Hirsch MW, Smale S, Devaney RL. Differential Equations, Dynamical Systems, and an Introduction to Chaos. Amsterdam, the Netherlands: Elsevier, 2004
Kadalbajoo MK, Gupta V. A brief survey on numerical methods for solving singularly perturbed problems. Appl Math Comput 2010; 217: 3641-3716
Kadalbajoo MK, Reddy YN. Numerical treatment of singularly perturbed two point boundary value problems. Appl Math Comput 1987; 21: 93-110