1-boyutlu düzenli uzun dalga denkleminin sayısal çözümü
Küçük Resim Yok
Tarih
2025
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
İnönü Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu tez altı bölümden olu¸smaktadır. Birinci bölümde RLW denklemi hakkında literatür taraması yapılarak tezde kullanılan temel kavramlar ve teoremler verildi. ?Ikinci bölümde sonlu fark yakla¸sımlarından ve iyi tanımlı bir ba¸slangıç deger problemi için ? tek ve çok adım yöntemlerinin bazılarından bahsedildi. Üçüncü bölümde RLW denkleminin sayısal çözümlerinin elde edildigi test problemleri ? tanımlanarak korunum sabitleri verildi. Dördüncü bölümde RLW denklemi Crank-Nicolson yöntemine göre ayrıkla¸stırıldı. Daha sonra lineer olmayan terim Rubin-Graves lineerle¸stirmesi ile lineerle¸stirildi ve sonlu fark yakla¸sımları uygulanarak bir sayısal ¸sema elde edildi. Elde edilen sayısal ¸sema ile test problemlerinin sayısal çözümleri bulundu. Be¸sinci bölümde RLW denklemi Adams-Bashforth yöntemine göre ayrıkla¸stırıldı. Daha sonra sonlu fark yakla¸sımları uygulanarak iki sayısal ¸sema elde edildi. Elde edilen sayısal ¸semalar ile test problemlerinin sayısal çözümleri bulundu. Son olarak altıncı bölümde elde edilen ¸semaların kar¸sıla¸stırılması yapılarak sonuçlar degerlendirildi. ? Anahtar Kelimeler: Düzenli Uzun Dalga Denklemi, Sonlu Farklar, Çok Adım Yöntemleri
This thesis consists of six chapters. In the first chapter, a literature review on the RLW equation is given and the basic concepts and theorems used in the thesis are given. In the second chapter, finite difference approximations and some of the single and multi-step methods for a well-defined initial value problem are discussed. In the third chapter, test problems for which numerical solutions of the RLW equation are obtained are defined and the conservation constants are given. In the fourth section, the RLW equation is discretized according to the Crank-Nicolson method. Then the nonlinear term is linearized by Rubin-Graves linearization and a numerical scheme is obtained by applying finite difference approximations. With the obtained numerical scheme, numerical solutions of the test problems were found. In the fifth section, the RLW equation is discretized according to the Adams-Bashforth method. Then, two numerical schemes were obtained by applying finite difference approximations. With the obtained numerical schemes, numerical solutions of the test problems were found. Finally, in the sixth section, the results are evaluated by comparing the obtained schemes. Keywords: Regularized Long Wave Equation, Finite Differences, Multistep Methods
This thesis consists of six chapters. In the first chapter, a literature review on the RLW equation is given and the basic concepts and theorems used in the thesis are given. In the second chapter, finite difference approximations and some of the single and multi-step methods for a well-defined initial value problem are discussed. In the third chapter, test problems for which numerical solutions of the RLW equation are obtained are defined and the conservation constants are given. In the fourth section, the RLW equation is discretized according to the Crank-Nicolson method. Then the nonlinear term is linearized by Rubin-Graves linearization and a numerical scheme is obtained by applying finite difference approximations. With the obtained numerical scheme, numerical solutions of the test problems were found. In the fifth section, the RLW equation is discretized according to the Adams-Bashforth method. Then, two numerical schemes were obtained by applying finite difference approximations. With the obtained numerical schemes, numerical solutions of the test problems were found. Finally, in the sixth section, the results are evaluated by comparing the obtained schemes. Keywords: Regularized Long Wave Equation, Finite Differences, Multistep Methods
Açıklama
Anahtar Kelimeler
Matematik, Mathematics
