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Title: :  An Overview of Numerical and Analytical Methods for Solving Ordinary Differential Equations
PaperId: :  14086
Published in:   International Journal Of Advance Research And Innovative Ideas In Education
Publisher:   IJARIIE
e-ISSN:   2395-4396
Volume/Issue:    Volume 4 Issue 2 2018
DUI:    16.0415/IJARIIE-14086
Licence: :   IJARIIE is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Author NameAuthor Institute
Pramod AnandraoResearch Scholar
Dr. Rakesh KoushalResearch Supervisor, Chaudhary Charansingh University, Meerut

Abstract

Mathematics
Differential Equation, Analytical Methods, Numerical, Independent, Ordinary Differential Equation Variable.
Differential Equations are among the most important Mathematical tools used in creating models in the science, engineering, economics, mathematics, physics, aeronautics, astronomy, dynamics, biology, chemistry, medicine, environmental sciences, social sciences, banking and many other areas A differential equation that has only one independent variable is called an Ordinary Differential Equation (ODE), and all derivatives in it are taken with respect to that variable. Most often, the variable is time, t; although, I will use x in this paper as the independent variable. The differential equation where the unknown function depends on two or more variables is referred to as Partial Differential Equations (PDE). In this paper, researcher presents the basic and commonly used numerical and analytical methods of solving ordinary differential equations. The results of these efforts are shown in the last sections of this chapter. We present theorems describing the existence and uniqueness of solutions to a wide class of first order differential equations.

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IJARIIE Pramod Anandrao, and Dr. Rakesh Koushal. "An Overview of Numerical and Analytical Methods for Solving Ordinary Differential Equations" International Journal Of Advance Research And Innovative Ideas In Education Volume 4 Issue 2 2018 Page 5090-5095
MLA Pramod Anandrao, and Dr. Rakesh Koushal. "An Overview of Numerical and Analytical Methods for Solving Ordinary Differential Equations." International Journal Of Advance Research And Innovative Ideas In Education 4.2(2018) : 5090-5095.
APA Pramod Anandrao, & Dr. Rakesh Koushal. (2018). An Overview of Numerical and Analytical Methods for Solving Ordinary Differential Equations. International Journal Of Advance Research And Innovative Ideas In Education, 4(2), 5090-5095.
Chicago Pramod Anandrao, and Dr. Rakesh Koushal. "An Overview of Numerical and Analytical Methods for Solving Ordinary Differential Equations." International Journal Of Advance Research And Innovative Ideas In Education 4, no. 2 (2018) : 5090-5095.
Oxford Pramod Anandrao, and Dr. Rakesh Koushal. 'An Overview of Numerical and Analytical Methods for Solving Ordinary Differential Equations', International Journal Of Advance Research And Innovative Ideas In Education, vol. 4, no. 2, 2018, p. 5090-5095. Available from IJARIIE, http://ijariie.com/AdminUploadPdf/An_Overview_of_Numerical_and_Analytical_Methods_for_Solving_Ordinary_Differential_Equations_ijariie14086.pdf (Accessed : ).
Harvard Pramod Anandrao, and Dr. Rakesh Koushal. (2018) 'An Overview of Numerical and Analytical Methods for Solving Ordinary Differential Equations', International Journal Of Advance Research And Innovative Ideas In Education, 4(2), pp. 5090-5095IJARIIE [Online]. Available at: http://ijariie.com/AdminUploadPdf/An_Overview_of_Numerical_and_Analytical_Methods_for_Solving_Ordinary_Differential_Equations_ijariie14086.pdf (Accessed : )
IEEE Pramod Anandrao, and Dr. Rakesh Koushal, "An Overview of Numerical and Analytical Methods for Solving Ordinary Differential Equations," International Journal Of Advance Research And Innovative Ideas In Education, vol. 4, no. 2, pp. 5090-5095, Mar-App 2018. [Online]. Available: http://ijariie.com/AdminUploadPdf/An_Overview_of_Numerical_and_Analytical_Methods_for_Solving_Ordinary_Differential_Equations_ijariie14086.pdf [Accessed : ].
Turabian Pramod Anandrao, and Dr. Rakesh Koushal. "An Overview of Numerical and Analytical Methods for Solving Ordinary Differential Equations." International Journal Of Advance Research And Innovative Ideas In Education [Online]. volume 4 number 2 ().
Vancouver Pramod Anandrao, and Dr. Rakesh Koushal. An Overview of Numerical and Analytical Methods for Solving Ordinary Differential Equations. International Journal Of Advance Research And Innovative Ideas In Education [Internet]. 2018 [Cited : ]; 4(2) : 5090-5095. Available from: http://ijariie.com/AdminUploadPdf/An_Overview_of_Numerical_and_Analytical_Methods_for_Solving_Ordinary_Differential_Equations_ijariie14086.pdf
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