Öz This article focuses on the numerical approximate solution of singularly perturbed systems of second-order reaction-diffusion two-point boundary-value problems for ordinary differential equations. To handle these types of problems, a numerical-asymptotic hybrid method has been used. In this hybrid approach, an efficient asymptotic method, the so-called successive complementary expansion method (SCEM) is employed first, and then a numerical method based on finite differences is applied to approximate the solution of corresponding singularly perturbed reaction-diffusion systems. Two illustrative examples are provided to demonstrate the efficiency, robustness, and easy applicability of the present method with convergence properties.

Anahtar Kelimeler:
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Singular perturbation problems,
reaction-diffusion equations,
asymptotic approximations,
boundary layers,
finite difference method

Bibtex | `@ { tbtkmath575276, journal = {Turkish Journal of Mathematics}, issn = {1300-0098}, eissn = {1303-6149}, address = {}, publisher = {TÜBİTAK}, year = {2019}, volume = {43}, pages = {460 - 472}, doi = {}, title = {An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusion boundary-value problems}, key = {cite}, author = {Cengizci, Süleyman and Natesan, Srinivasan and Atay, Mehmet Tarik} }` |

APA | Cengizci, S , Natesan, S , Atay, M . (2019). An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusion boundary-value problems . Turkish Journal of Mathematics , 43 (1) , 460-472 . |

MLA | Cengizci, S , Natesan, S , Atay, M . "An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusion boundary-value problems" . Turkish Journal of Mathematics 43 (2019 ): 460-472 < |

Chicago | Cengizci, S , Natesan, S , Atay, M . "An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusion boundary-value problems". Turkish Journal of Mathematics 43 (2019 ): 460-472 |

RIS | TY - JOUR T1 - An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusion boundary-value problems AU - Süleyman Cengizci , Srinivasan Natesan , Mehmet Tarik Atay Y1 - 2019 PY - 2019 N1 - DO - T2 - Turkish Journal of Mathematics JF - Journal JO - JOR SP - 460 EP - 472 VL - 43 IS - 1 SN - 1300-0098-1303-6149 M3 - UR - Y2 - 2021 ER - |

EndNote | %0 Turkish Journal of Mathematics An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusion boundary-value problems %A Süleyman Cengizci , Srinivasan Natesan , Mehmet Tarik Atay %T An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusion boundary-value problems %D 2019 %J Turkish Journal of Mathematics %P 1300-0098-1303-6149 %V 43 %N 1 %R %U |

ISNAD | Cengizci, Süleyman , Natesan, Srinivasan , Atay, Mehmet Tarik . "An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusion boundary-value problems". Turkish Journal of Mathematics 43 / 1 (Şubat 2019): 460-472 . |

AMA | Cengizci S , Natesan S , Atay M . An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusion boundary-value problems. Turkish Journal of Mathematics. 2019; 43(1): 460-472. |

Vancouver | Cengizci S , Natesan S , Atay M . An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusion boundary-value problems. Turkish Journal of Mathematics. 2019; 43(1): 460-472. |

IEEE | S. Cengizci , S. Natesan ve M. Atay , "An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusion boundary-value problems", Turkish Journal of Mathematics, c. 43, sayı. 1, ss. 460-472, Şub. 2019 |

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