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Step Size Strategies Based On Error Analysis For The Linear Systems

Year 2011, Volume: 6 Issue: 2, 149 - 159, 01.12.2011

Abstract

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 orderm. We have also give the numerical examples.

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.

Lineer Sistemler İçin Hata Analizi Tabanlı Adım Genişliği Stratejileri

Year 2011, Volume: 6 Issue: 2, 149 - 159, 01.12.2011

Abstract

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.

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.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Makaleler
Authors

Gülnur Çelik Kızılkan This is me

Kemal Aydın

Publication Date December 1, 2011
Published in Issue Year 2011 Volume: 6 Issue: 2

Cite

IEEE G. Çelik Kızılkan and K. Aydın, “Step Size Strategies Based On Error Analysis For The Linear Systems”, Süleyman Demirel University Faculty of Arts and Science Journal of Science, vol. 6, no. 2, pp. 149–159, 2011.