Nonlineer diferansiyel denklemlerin yakınsaklığı
Küçük Resim Yok
Tarih
1992
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Trakya Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
ÖZET Bu çalışmada, birinci bölümde diferansiyel denklemlerin genel kavramları verilerek sınıflandırması yapıldı. Non- lineer denlemler tanıtılarak tezin esas konusu olan nonlineer parabolik denklemler anlatıldı. ikinci bölümde nonlineer denklemlerin çözümleri hakkında bilgi verilerek sayısal çözümler anlatıldı ve bu çözümler esnasında meydana gelen hatalar belirtildi. Sayısal çözüm metodlarmdan sonlu farklar anlatıldı ve sonlu farklarda önemli olan yakınsaklık ve stabilite kavramları verildi, üçüncü bölümde ağırlıklı ortalama yaklaşımı ifade edilerek üt = Uxx denklemine tatbik edildi. Bu yaklaşım altında denkleme Richtmayer linerizasyon metodu uygulanarak yakınsaklık ve stabilitesi incelendi. Dördüncü bölümde üç zaman seviyeli explicit metod ifade edilerek a+l Ut = c UXx denklemine tatbik edildi. Bu yaklaşım altında yakınsaklık ve stabilitesi incelendi.
ii SUMMARY In the first part of this study, general notions of the differential equations were introduced and their classifica tions were made. Then, introducing the non-linear equations, the subject of my thesis non-linear parabolic equations were presented. In the second part, the solutions of non-linear equations and errors seen during the applications of the solutions were indicated and also numerical solutions were told. Finite differences of the numerical solutions were introduced, convergence and stability notions having an impor tance in finite-difference equations were presented... In the third part, a weighted average approximation was desc- m ribed and applied to the equation Ut » Uxx. With the help of this approximation, Richtmayer Linerizasyon method was applied to that equation and also its convergence and stabi lity were studied. In the fourth part, three time-level exp licit method was described and applied to the equation a+ i Ut = cUxx and also with the help of that approximation its convergence and stability were studied.
ii SUMMARY In the first part of this study, general notions of the differential equations were introduced and their classifica tions were made. Then, introducing the non-linear equations, the subject of my thesis non-linear parabolic equations were presented. In the second part, the solutions of non-linear equations and errors seen during the applications of the solutions were indicated and also numerical solutions were told. Finite differences of the numerical solutions were introduced, convergence and stability notions having an impor tance in finite-difference equations were presented... In the third part, a weighted average approximation was desc- m ribed and applied to the equation Ut » Uxx. With the help of this approximation, Richtmayer Linerizasyon method was applied to that equation and also its convergence and stabi lity were studied. In the fourth part, three time-level exp licit method was described and applied to the equation a+ i Ut = cUxx and also with the help of that approximation its convergence and stability were studied.
Açıklama
Yüksek Lisans
Anahtar Kelimeler
Matematik, Mathematics
