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Order of convergence and stability of evolution operator method

Evrim operatörü metodunun yakınsama mertebesi ve stabilite özellikleri

  1. Tez No: 35497
  2. Yazar: A.İHSAN HOŞÇELİK
  3. Danışmanlar: YRD. DOÇ. DR. TANIL ERGENÇ
  4. Tez Türü: Doktora
  5. Konular: Matematik, Mathematics
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 1994
  8. Dil: İngilizce
  9. Üniversite: Orta Doğu Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Matematik Ana Bilim Dalı
  12. Bilim Dalı: Belirtilmemiş.
  13. 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

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