THE ANALYSIS OF THE EFFECT OF THE NORMS IN THE STEP SIZE SELECTION FOR THE NUMERICAL INTEGRATION
Year 2016,
Volume: 4 Issue: 2, 116 - 123, 01.10.2016
GULNUR CELIK Kızılkan
,
AHMET Duman
,
KEMAL Aydın
Abstract
In scientific studies involving norm calculations, the choice of the norm affects the obtained results. We have aimed to examine the behavior of the step sizes using different norms and norm inequalities in step size strategy obtained in \cite{Kızılkan 1} for linear Cauchy problems.
References
- [1] Celik Kizilkan, G. and Aydn, K., Step Size Strategies Based on Error Analysis for The Linear Systems, SDU Journal of Science (e-journal), Vol:6, No.2 (2011), 149-159.
- [2] Celik Kizilkan, G.,Step size strategies on the numerical integration of the systems of differential equations,Ph.D. Thesis, Graduate Natural and Applied Sciences, Seluk University, Konya, 2009 (in Turkish).
- [3] Celik Kizilkan, G.,On the nding of step size in the numerical integration of initial value problem,Master Thesis, Graduate Natural and Applied Sciences, Seluk University, Konya, 2004 (in Turkish).
- [4] Celik Kizilkan, G. and Aydin, K.,Step Size Strategy Based on Error Analysis, SUFEFD, Vol: 25 (2005), 79-86 (in Turkish).
- [5] Golub, G. H. and Van Loan, C.F., Matrix Computations, third edition, The Johns Hopkins University Press, London, 1996.
- [6] Quarteroni, A., Sacco, R. and Saleri, F.,Numerical Mathematics, Springer Verlag, New York, 2000.
- [7] Bulgak, A. and Bulgak, H.,Linear Algebra, Seluk University Applied Mathematics Research Center Publications, Konya, 2001.
- [8] Tasci, D.,Linear Algebra, Gazi Bookstore, Ankara, 2005.
- [9] Chapra, S.C. and Canale, R.P., Numerical methods for engineers, sixth edition, McGraw Hill, New York, 2010.
- [10] Acton, A.C., A brief overview of the condition number (25 October 2008). http://ansys.net/ansys/tips/acton20080825-condition number.pdf (Access date: 17.04.2016)
Year 2016,
Volume: 4 Issue: 2, 116 - 123, 01.10.2016
GULNUR CELIK Kızılkan
,
AHMET Duman
,
KEMAL Aydın
References
- [1] Celik Kizilkan, G. and Aydn, K., Step Size Strategies Based on Error Analysis for The Linear Systems, SDU Journal of Science (e-journal), Vol:6, No.2 (2011), 149-159.
- [2] Celik Kizilkan, G.,Step size strategies on the numerical integration of the systems of differential equations,Ph.D. Thesis, Graduate Natural and Applied Sciences, Seluk University, Konya, 2009 (in Turkish).
- [3] Celik Kizilkan, G.,On the nding of step size in the numerical integration of initial value problem,Master Thesis, Graduate Natural and Applied Sciences, Seluk University, Konya, 2004 (in Turkish).
- [4] Celik Kizilkan, G. and Aydin, K.,Step Size Strategy Based on Error Analysis, SUFEFD, Vol: 25 (2005), 79-86 (in Turkish).
- [5] Golub, G. H. and Van Loan, C.F., Matrix Computations, third edition, The Johns Hopkins University Press, London, 1996.
- [6] Quarteroni, A., Sacco, R. and Saleri, F.,Numerical Mathematics, Springer Verlag, New York, 2000.
- [7] Bulgak, A. and Bulgak, H.,Linear Algebra, Seluk University Applied Mathematics Research Center Publications, Konya, 2001.
- [8] Tasci, D.,Linear Algebra, Gazi Bookstore, Ankara, 2005.
- [9] Chapra, S.C. and Canale, R.P., Numerical methods for engineers, sixth edition, McGraw Hill, New York, 2010.
- [10] Acton, A.C., A brief overview of the condition number (25 October 2008). http://ansys.net/ansys/tips/acton20080825-condition number.pdf (Access date: 17.04.2016)