The finite difference method on adaptive mesh for singularly perturbed nonlinear 1D reaction diffusion boundary value problems

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Atıf İçin Kopyala

DURU H., Güneş B.

Journal of Applied Mathematics and Computational Mechanics, cilt.19, sa.4, ss.45-56, 2020 (Hakemli Dergi)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 19 Sayı: 4
• Basım Tarihi: 2020
• Doi Numarası: 10.17512/jamcm.2020.4.04
• Dergi Adı: Journal of Applied Mathematics and Computational Mechanics
• Sayfa Sayıları: ss.45-56
• Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this paper, we study singularly perturbed nonlinear reaction-diffusion equations. The asymptotic behavior of the solution is examined. The difference scheme which is accomplished by the method of integral identities with using of interpolation quadrature rules with weight functions and remainder term integral form is established on adaptive mesh. Uniform convergence and stability of the difference method are discussed in the discrete maximum norm. The discrete scheme shows that orders of convergent rates are close to 2. An algorithm is presented, and some problems are solved to validate the theoretical results.