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Title: :  A Study on Numerical and Analytical Methods for Solving Ordinary Differential Equations
PaperId: :  18747
Published in:   International Journal Of Advance Research And Innovative Ideas In Education
Publisher:   IJARIIE
e-ISSN:   2395-4396
Volume/Issue:    Volume 7 Issue 6 2021
DUI:    16.0415/IJARIIE-18747
Licence: :   IJARIIE is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Author NameAuthor Institute
Kudke Pawanraj ShivmurtiResearch Scholar, Sunrise University, Alwar, Rajasthan
Dr. Sudesh KumarAssitant Professor Sunrise University, Alwar, Rajasthan

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 Kudke Pawanraj Shivmurti, and Dr. Sudesh Kumar. "A Study on Numerical and Analytical Methods for Solving Ordinary Differential Equations" International Journal Of Advance Research And Innovative Ideas In Education Volume 7 Issue 6 2021 Page 1772-1777
MLA Kudke Pawanraj Shivmurti, and Dr. Sudesh Kumar. "A Study on Numerical and Analytical Methods for Solving Ordinary Differential Equations." International Journal Of Advance Research And Innovative Ideas In Education 7.6(2021) : 1772-1777.
APA Kudke Pawanraj Shivmurti, & Dr. Sudesh Kumar. (2021). A Study on Numerical and Analytical Methods for Solving Ordinary Differential Equations. International Journal Of Advance Research And Innovative Ideas In Education, 7(6), 1772-1777.
Chicago Kudke Pawanraj Shivmurti, and Dr. Sudesh Kumar. "A Study on Numerical and Analytical Methods for Solving Ordinary Differential Equations." International Journal Of Advance Research And Innovative Ideas In Education 7, no. 6 (2021) : 1772-1777.
Oxford Kudke Pawanraj Shivmurti, and Dr. Sudesh Kumar. 'A Study on Numerical and Analytical Methods for Solving Ordinary Differential Equations', International Journal Of Advance Research And Innovative Ideas In Education, vol. 7, no. 6, 2021, p. 1772-1777. Available from IJARIIE, https://ijariie.com/AdminUploadPdf/A_Study_on_Numerical_and_Analytical_Methods_for_Solving_Ordinary_Differential_Equations_ijariie18747.pdf (Accessed : 08 May 2025).
Harvard Kudke Pawanraj Shivmurti, and Dr. Sudesh Kumar. (2021) 'A Study on Numerical and Analytical Methods for Solving Ordinary Differential Equations', International Journal Of Advance Research And Innovative Ideas In Education, 7(6), pp. 1772-1777IJARIIE [Online]. Available at: https://ijariie.com/AdminUploadPdf/A_Study_on_Numerical_and_Analytical_Methods_for_Solving_Ordinary_Differential_Equations_ijariie18747.pdf (Accessed : 08 May 2025)
IEEE Kudke Pawanraj Shivmurti, and Dr. Sudesh Kumar, "A Study on Numerical and Analytical Methods for Solving Ordinary Differential Equations," International Journal Of Advance Research And Innovative Ideas In Education, vol. 7, no. 6, pp. 1772-1777, Nov-Dec 2021. [Online]. Available: https://ijariie.com/AdminUploadPdf/A_Study_on_Numerical_and_Analytical_Methods_for_Solving_Ordinary_Differential_Equations_ijariie18747.pdf [Accessed : 08 May 2025].
Turabian Kudke Pawanraj Shivmurti, and Dr. Sudesh Kumar. "A Study on Numerical and Analytical Methods for Solving Ordinary Differential Equations." International Journal Of Advance Research And Innovative Ideas In Education [Online]. volume 7 number 6 (08 May 2025).
Vancouver Kudke Pawanraj Shivmurti, and Dr. Sudesh Kumar. A Study on Numerical and Analytical Methods for Solving Ordinary Differential Equations. International Journal Of Advance Research And Innovative Ideas In Education [Internet]. 2021 [Cited : 08 May 2025]; 7(6) : 1772-1777. Available from: https://ijariie.com/AdminUploadPdf/A_Study_on_Numerical_and_Analytical_Methods_for_Solving_Ordinary_Differential_Equations_ijariie18747.pdf
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