ANALYSIS AND COMPARATIVE STUDY OF NUMERICAL METHODS TO SOLVE ORDINARY DIFFERENTIAL EQUATION WITH INITIAL VALUE PROBLEM.
- Assistant Professor at Sarepul Institute of Higher Education.
- Cite This Article as
- Corresponding Author
Since mathematics is a science of communication between us and the scientific sciences, in particular it introduces all the rules and problems as formulas, and searches for a solution. A part of the mathematics that is widely used in all sciences is the differential equation that will be studied in this dissertation. Each parts of these equations has its own method for solving, and we have generally studied the analytic methods in the calculus, and here we will introduce the numerical solutions. It is worth noting that in analytic methods cannot gives solution, for all equations this is where scientists have discovered the numerical methods that can be solved by those methods for those equations that are not solved in an analytical methods.In this Article, we first introduce differential equations and introduce a number of elementary topics for introduction so that the reader will get acquainted with these definitions and issues before the start of the process.Later in this article, one basic methods will be studied, the single step method, respectively, which relate to the initial value problem.Here we will examine in detail and analyze all the ways in which these methods are available.In the next step, all the good nesses, advantages, disadvantages that exist between these methodswill be discussed, and also a comparative study we will have in this paper.
- Shawagfeh and D. Kaya, Comparing Numerical Methods for Solution of Systems of ODE, Applied Mathematics Letters, Vol 17, pp 323-328, 2004.
- Nikos E Mastorakis, Numerical Solution of non Linear Ordinary Differential Equations Via Collocation Method ( Finite Elements) and Genetic Algorithms, Conf. on Evolutionary Computing, pp 36-42, 2005.
- Fadugba S.E and et al, On the Comparative Study of Some Numerical Methods for the Solution of initial value problems in ODE, International Journal of Innovation in Science and Mathematics, Vol 2, pp 61-67, 2010.
- Ochoche ABRAHAM and Gbolahan BOLARIN, On Error Estimation in Runge Kutta Methods, Leonardo Journal of Science, Vol 1, pp 1-10, 2011.
- Steven C Chapra, Applied Numerical Methods with MATLAB for engineering and science, McGraw Hill, third Edition, 2012.
- K.Jain and et al, Numerical Methods for scientific and Engineering computation, New age international publication, Sixth Edition, 2012
- Ogunrinde R. Bosede and et al, On Some Numerical Methods for Solving Initial Value Problems in ODE, IOSR journal of Mathematics, Vol 1, pp 25-31, 2012.
- Amirul Islam, A comparative Study on Numerical Solutions of Initial value problems for Ordinary Differential Equations with Euler and Runge Kutta Methods, American Journal of Computational Mathematics, Vol 5, pp 393- 404, 2015.
- Somayeh Ezadi and et al, Numerical Solution of ODEs Based on Semi ? Taylor by Neural Network improvement, Science Journal, Vol 36, pp 2584- 2589, 2015.
- Sankar Prasad Mondal and et al, Numerical Solution of First Order Linear Differential Equation in Fuzzy Environment by Runge Kutta-Fehlberg Method and Its Application, International Journal of Differential Equation, pp 1-15, 2016.
- Gadamsetty Revathi, Numerical Solution of Ordinary Differential Equation and Application, International Journal of Management and Applied Science, Vol 3, pp 1-5, 2017.
- C Senthilnathan, A Numerical Solution of Initial value problem For ODE with Euler and Higher Order of Runge Kutta Methods using MATLAB, International Journal of Engineering Science Invention, Vol 7, pp 25-31, 2018.
[Nikzad Jamali. (2019); ANALYSIS AND COMPARATIVE STUDY OF NUMERICAL METHODS TO SOLVE ORDINARY DIFFERENTIAL EQUATION WITH INITIAL VALUE PROBLEM. Int. J. of Adv. Res. 7 (5). 117-128] (ISSN 2320-5407). www.journalijar.com
Assistant Professor at Sarepul Institute of Higher Education.
Article DOI: 10.21474/IJAR01/9010 DOI URL: http://dx.doi.org/10.21474/IJAR01/9010
Share this article
This work is licensed under a Creative Commons Attribution 4.0 International License.