Numerical Solutions of the Singularly Perturbed Semilinear Delay Differential Equations

Year 2022, , 330 - 343, 30.08.2022

Hakkı Duru , Bahar Gürbüz

https://doi.org/10.53433/yyufbed.1085501

Abstract

In this study, the numerical solution of the singularly perturbed quasilinear differential equations with constant delay is investigated by the method of integral identities with use of linear basis functions and interpolating quadrature formulas, a finite difference scheme is established on Boglaev-Bakhvalov type mesh. The error approximations are obtained in the discrete maximum norm. A numerical example is solved to clarify the theoretical analysis.

Keywords

Bakhvalov mesh, Difference scheme, Singular perturbation, Uniform convergence

Singüler Pertürbe Özellikli Yarılineer Gecikmeli Diferansiyel Denklemlerin Nümerik Çözümleri

Abstract

Bu çalışmada sabit gecikme içeren singüler pertürbe özellikli kuasilineer diferansiyel denklemlerin nümerik çözümleri araştırılmıştır. Lineer baz fonksiyonları ve interpolasyon kuadratür kurallarını kullanarak Boglaev-Bakhvalov tipli şebeke üzerinde sonlu fark şeması kurulmuştur. Ayrık maksimum normda hata yaklaşımları elde edilmiştir. Teorik analizi doğrulamak için bir adet nümerik örnek çözülmüştür.

Keywords

Bakhvalov şebeke, Düzgün yakınsaklık, Fark şeması, Singüler pertürbasyon

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