Web Application for Step Size Strategies

Abstract

In this study,  it has been designed an interactive web interface which provides the online use of step size strategies to obtain the numerical solutions of Cauchy problems.  This web interface has been created by using Django web framework of Python programming language.

Keywords

• step size strategies,variable step size,numerical solution,web interface,python,django

References

1. [1] G. Bastin, Lectures on mathematical modelling of biological systems, https://perso.uclouvain.be/georges.bastin/lectures-bio.pdf, 2012, (Access date: 24.11.2018).
2. [2] W.A. Brock, A.G. Malliaris, Differential Equations, Stabiltiy and Chaos in Dynamic Economics, Elseiver Science Publishers, Amsterdam, 1989.
3. [3] R. L. Burden, J. D. Faires, Numerical Analysis, Ninth Edition, Richard Stratton, 2010.
4. [4] Calculator for general first order differential equations, http://elsenaju.eu/Calculator/ODE-General-first-Order.htm, 2011, (Access date:21/04/2019).
5. [5] G. Celik Kızılkan, K. Aydın, A new variable step size algorithm for cauchy problem, Applied Mathematics and Computation, volume 183, (2006), pp. 878–884.
6. [6] G. Celik Kızılkan, K. Aydın, Step size strategy based on error analysis,SDU Journal of Science (E-Journal), volume 25, (2015), pp. 79–86.
7. [7] G. Celik Kızılkan, On the finding of step size in the numerical integration of initial value problem, Selc¸uk University Graduate School of Natural and Applied Sciences Department of Mathematics, Master Thesis, 2004.
8. [8] G. Celik Kızılkan, Step size strategies on the numerical integration of the systems of differential equations, Selc¸uk University Graduate School of Natural and Applied Sciences Department of Mathematics, Ph.D., 2009.

9. [9] G. Celik Kızılkan, Step size strategies based on error analysis for the linear systems, SDU Journal of Science (E-Journal), volume 25, (2011), pp. 149–159.
10. [10] G. Celik Kızılkan, K. Aydın, Step size strategies for the numerical integration of systems of differential equations, Journal of Computational and Applied Mathematics, volume 236, (2012), pp. 3805–3816.
11. [11] G. Celik Kızılkan, A. Duman, K. Aydın, The analysis of the effect of the norms in the step size selection for the numerical integration, Konuralp Journal of Mathematics, volume 4, (2016), pp. 116–123.
12. [12] G. C¸ elik Kızılkan, A. Duman, K. Aydın, Analysis with variable step size strategy of some sir epidemic models, Karaelmas Fen ve M¨uhendislik Dergisi, volume 6, (2016), pp. 203–210.
13. [13] A. Downey, Think python, Green Tea Press, 2012.
14. [14] EMathHelp, http://www.emathhelp.net/calculators/differential-equations/euler-method-calculator/, 2018, (Access date:21/04/2019).
15. [15] H. Fangohr, Introduction to python for computational science and engineering, Faculty of Engineering and the Environment University of Southampton, 2015.
16. [16] I. Farago, Numerical Methods for Ordinary Differential Equations, 2013.
17. [17] First Order Differential Equation Solver, http://www.math-cs.gordon.edu/%7esenning/desolver, 2009, (Access date:21/04/2019).
18. [18] I. Farag´o, Numerical Methods for Ordinary Differential Equations, 2013.
19. [19] O. Golberg, Adaptive stepsize numerical methods for solving ordinary differential equations, (2007).
20. [20] T. Harko, S.N.F. Lobo, M.K. Mak, Exact analyitical solutions of the susceptible- infected- recovered (sir) epidemic model and of the sir model with equal death and birth dates, Appl. Math. Comput., volume 236, (2014), pp. 84–94.
21. [21] T. Harko, S.N.F. Lobo, M.K. Mak, The mathematics of infectious diseases, SIAM Review, volume 42, (2014), pp. 599–653.
22. [22] M.T. Heath, Scientific Computing an Introductory Survey, Second Edition, McGraw-Hill, New York, 2002.
23. [23] A. Hourieh, Learning Website Development with Django, Packt Publishing, 2008.
24. [24] A. Jorba, M. Zou, A software package for the numerical integration of odes by means of high-order taylor methods, (2004).
25. [25] Keisan Online Calculator, https://keisan.casio.com/exec/system/1392171850, 2018, (Access date:21/04/2019).
26. [26] H.P. Langtangen, Numerical python, Simula Research Laboratory Dept. of Informatics, Univ. of Oslo, 2008.
27. [27] MathsTools, https://www.mathstools.com/, 2012, (Access date:21/04/2019).
28. [28] I. Ozsvald, M. Gorelick, High Performance Python, O’Reilly Media, 2014.
29. [29] Two Dimensional Differential Equation Solver and Grapher V 1.0, https://www.zweigmedia.com/RealWorld/deSystemGrapher/func.html, 2018, (Access date:21/04/2019).
30. [30] N. Waeleh, Z.A. Majid, F. ˙Ismail, M. Suleiman, Numerical solution of higher order ordinary differential equations by direct block code, Journal of Mathematics and Statistics, volume 8, (2012), pp. 77–81.
31. [31] M. Yuksektepe, A turkish guide about Django, 2016.