Order of convergence and stability of evolution operator method
Evrim operatörü metodunun yakınsama mertebesi ve stabilite özellikleri
- Tez No: 35497
- Danışmanlar: YRD. DOÇ. DR. TANIL ERGENÇ
- Tez Türü: Doktora
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1994
- Dil: İngilizce
- Üniversite: Orta Doğu Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Matematik Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 78
Özet
ABSTRACT ORDER OF CONVERGENCE AND STABILITY OF EVOLUTION OPERATÖR METHOD HASÇELİK, A. ihsan Ph.D. in Mathematics Supervisor : Asst.Prof.Dr. Tanıl ERGENÇ September, 1994, 67 pages. Evolution Operatör Method ([14],[16]) is used either as an analytic method ör as a nonlinear one-step numerical method for solving Ordinary Differential Equations (ÖDE). When this method is applied to an initial value problem,it requires the computation of the dynamical coefficients, spectral coeffients, eigenvalues kNJi, and residues R^. The computation of the dynamical coefficients and especially spectral coefficients for an arbitrary ÖDE system is rather difficult, which is explained in [15]. in [16] and [1] some techniques are developed to calculate these coefficients for the systems with polynomial right hand side functions. in this study, the order of convergence of Evolution Operatör Method is obtained. Also the stability characteristics of the method are given for. some special values of approximation order. A recursive formulation of the dynamical and spectral coefficients for ÖDE systems whose right hand-side functions are not only polynomials but in the form of products of polynomials and exponential functions is developed. A new algorithm for the calculation of A^ and RNık is presented. This new algorithm is compared with the previously published algorithms. The numerical applications of the algorithms presented here and previously iiidinamik ve spektral katsayılar ile \NJc ve RNk lan hesaplamaya yarıyan (yukarıda bahsedilen) algoritmaları Lotka-Volterra denklem sistemine uygulanmış ve bu sistem için nümerik çözümler elde edilmiştir. Anahtar Kelimeler : Evrim Operatörü Metodu, Adi diferansiyel denklemler için nümerik metodlar, Yakınsama mertebesi, Nümerik Kararlılık Bilim Dalı Sayısal Kodu : 403.06.01 vı
Özet (Çeviri)
ABSTRACT ORDER OF CONVERGENCE AND STABILITY OF EVOLUTION OPERATÖR METHOD HASÇELİK, A. ihsan Ph.D. in Mathematics Supervisor : Asst.Prof.Dr. Tanıl ERGENÇ September, 1994, 67 pages. Evolution Operatör Method ([14],[16]) is used either as an analytic method ör as a nonlinear one-step numerical method for solving Ordinary Differential Equations (ÖDE). When this method is applied to an initial value problem,it requires the computation of the dynamical coefficients, spectral coeffients, eigenvalues kNJi, and residues R^. The computation of the dynamical coefficients and especially spectral coefficients for an arbitrary ÖDE system is rather difficult, which is explained in [15]. in [16] and [1] some techniques are developed to calculate these coefficients for the systems with polynomial right hand side functions. in this study, the order of convergence of Evolution Operatör Method is obtained. Also the stability characteristics of the method are given for. some special values of approximation order. A recursive formulation of the dynamical and spectral coefficients for ÖDE systems whose right hand-side functions are not only polynomials but in the form of products of polynomials and exponential functions is developed. A new algorithm for the calculation of A^ and RNık is presented. This new algorithm is compared with the previously published algorithms. The numerical applications of the algorithms presented here and previously iiipublished ones are given for the calculation of the dynamical coeffirients, spectral coeffitients, kNık and RNJf. For testing the algorithms mentioned above, the Lotka-Volterra system is used. Keywords : Evolution Operatör Method, Numerical methods for ÖDE systems, Order of convergence, Stability. Science Code : 403.06.01
Benzer Tezler
- Pressure analysis of wellbore using Lattice Boltzmann method
Lattıce Boltzmann yöntemiyle kuyuiçi basınç analizi
AMIR TOOSI
Yüksek Lisans
İngilizce
2016
Petrol ve Doğal Gaz Mühendisliğiİstanbul Teknik ÜniversitesiPetrol ve Doğal Gaz Mühendisliği Ana Bilim Dalı
DOÇ. DR. GÜRŞAT ALTUN
- Büyük boyutlu veriler için metasezgisel yöntemler ile öznitelik indirgemede yeni bir yaklaşım geliştirilmesi
Developing a new approach to feature selection with metaheuristic methods for large scale data
ESİN AYŞE ZAİMOĞLU
Doktora
Türkçe
2023
Bilgisayar Mühendisliği Bilimleri-Bilgisayar ve KontrolSakarya ÜniversitesiBilgisayar Mühendisliği Ana Bilim Dalı
DOÇ. DR. NİLÜFER YURTAY
- Alt-uzay dönüşüm yöntemi ile Fır süzgeç tasarımı
Finite-duration impulse response filter design using subspace transformations
MEHMET DEVRİM AZAK
Yüksek Lisans
Türkçe
1997
Elektrik ve Elektronik Mühendisliğiİstanbul Teknik ÜniversitesiElektronik-Haberleşme Eğitimi Ana Bilim Dalı
PROF. DR. ALİ NUR GÖNÜLEREN
- The generalized fractional Benjamin Bona Mahony equation: Analytical and numerical results
Genelleştirilmiş kesirli Benjamin Bona Mahony denklemi: Analitik ve sayısal sonuçlar
GÖKSU ORUÇ
Doktora
İngilizce
2021
Matematikİstanbul Teknik ÜniversitesiMatematik Mühendisliği Ana Bilim Dalı
PROF. DR. GÜLÇİN MİHRİYE MUSLU
DOÇ. DR. HANDAN BORLUK
- Sosyal katmanlar arasındaki ilişkileri temel alan ağırlıklı sosyal ağların modellenmesi
Modelling weighted social networks based on relationships between different social layers
EGEMEN BERKİ ÇİMEN
Yüksek Lisans
Türkçe
2014
Endüstri ve Endüstri MühendisliğiHava Harp Okulu KomutanlığıEndüstri Mühendisliği Ana Bilim Dalı
YRD. DOÇ. DR. MURAT ERMİŞ
YRD. DOÇ. DR. İLKER BEKMEZCİ