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Lineer Sistemler İçin Hata Analizi Tabanlı Adım Genişliği Stratejileri

Step Size Strategies Based On Error Analysis For The Linear Systems

Journal Name:

  • Süleyman Demirel Üniversitesi Fen Dergisi

Publication Year:

  • 2011

Key Words:

Keywords (Original Language):

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
In this paper, we have obtained the step size strategies for numerical integration of the linear differential equation systems. We have given the algorithms which calculate step sizes based on the given strategies and numerical solutions. These strategies and algorithms are generalized to systems by modifying the algorithm and strategy in [1]. We have applied our strategies to Cauchy problem with order m. We have also give the numerical examples.
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Abstract (Original Language): 
Bu çalışmada, lineer diferensiyel denklem sistemlerinin nümerik integrasyonu için adım genişliği stratejileri elde edilmiştir. Verilen stratejilere uygun olarak adım genişlikleri ve nümerik çözümler hesaplayan algoritmalar verilmiştir. Bu strateji ve algoritmalar [1] de verilen strateji ve algoritmanın değiştirilerek sistemlere genişletilmesidir. Verilen stratejiler m. mertebeden Cauchy problemine uygulanmıştır. Ayrıca, sonuçların doğruluğunu göstermek için nümerik örnekler de verilmiştir.
FULL TEXT (PDF): 
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  • 2
149-159
  • Turkish

REFERENCES

References: 

[1] Çelik Kızılkan G., 2004. On the finding of step size in the numerical integration of initial value problem, Master thesis, Graduate Natural and Applied Sciences, Selcuk University, Konya (in Turkish).
[2] Ban S.J., Lee C.L., Cho H., Kim S.W., 2010. A variable step-size adaptive algorithm for direct
frequency estimation, Signal Processing, 90: 2800-2805. [3] Çelik Kızılkan G., Aydın K., 2005. Step Size Strategy Based on Error Analysis, Selcuk University
Science and Art Faculty Journal of Science, 25: 79-86 (in Turkish). [4] Çelik Kızılkan G., Aydın K., 2006. A new variable step size algorithm for Cauchy problem, Applied
Mathematics and Computation, 183: 878-884. [5] Gear C.W., 1971. Numerical initial value problems in ordinary differential equations, Prentice- Hall,
New Jersey, 1971.
[6] Miranker W.L., 1981. Numerical methods for stiff equations and singular perturbation problems, D.
Rediel Publishing Company, Holland. [7] Shampine L.F., Allen R.C., Pruess S.,1996. Fundamentals of numerical computing, John Wiley&Sons,
INC, New York.
[8] Heath M.T., 2002. Scientific Computing an Introductory Survey, Second edition, McGraw-Hill, New
York.
[9] Loan C.F.V., 2000. Introduction to Scientific Computing, Prentice Hill, United States of America. [10] Gu M., 1998. Stable and Efficient Algorithms for Structured Systems of Linear Equations, SIMAX, 19(2), 279-306.
Kemal Aydın e-mail: kaydin@selcuk.edu.tr

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