Difference Schemes for the Singularly Perturbed Quasilinear Boundary Value Problems
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2021
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Bu çalışmada singüler pertürbe özellikli kuazilineer sınır değer problemleri ele alınmıştır. Bu bağlamda önce problemin çözümünün asimptotik davranışı incelenmiştir. Kalan terimi integral formunda olan interpolasyon kuadratür kuralları ve lineer baz fonksiyonları kullanılarak Bakhvalov ve Shishkin sebekeler üzerinde sonlu fark şeması kurulmuştur. Sunulan metodun yakınsaklık ve hata analizi yapılmıştır. Teorik sonuçlar nümerik örnekler üzerinde test edilmiştir.
İn this study, singularly perturbed quasilinear boundary value problems are considered. In this sense, firstly, the asymptotic behavior of the exact solution is investigated. The finite difference scheme which is accomplished by the method of integral identities with using of interpolating quadrature rules with linear basis functions remainder term in integral form is constructed both on Bakhvalov and Shishkin meshes. The convergence and error analysis of the presented method is carried out. Theoretical results are tested on numerical examples.
İn this study, singularly perturbed quasilinear boundary value problems are considered. In this sense, firstly, the asymptotic behavior of the exact solution is investigated. The finite difference scheme which is accomplished by the method of integral identities with using of interpolating quadrature rules with linear basis functions remainder term in integral form is constructed both on Bakhvalov and Shishkin meshes. The convergence and error analysis of the presented method is carried out. Theoretical results are tested on numerical examples.
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Matematik, Mathematics
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75