A mathematical equation which involves a function and its derivatives is called a differential equation. We consider a real life situation, from this form a mathematical model, solve that model using some mathematical concepts and take interpretation of solution. It is a well known and popular concept in mathematics because of its massive application in real world problems. Differential equations are one of the most important mathematical tools used in modeling problems in Physics, Biology, Economics, Chemistry, Engineering and medical Sciences. Differential equation can describe many situations viz exponential growth and de cay, the population growth of species, the change in investment return over time. We can solve differential equations using classical as well as numerical methods, In this paper we compare numerical methods of solving initial valued first order ordinary differential equations namely Euler method, Improved Euler method, Runge Kutta method and their accuracy level. We use here Scilab Software to obtain direct solution for these methods. Vibahvari Tukaram Dhokrat "Comparative Analysis of Different Numerical Methods for the Solution of Initial Value Problems in First Order Ordinary Differential Equations" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-5 , August 2021, URL: https://www.ijtsrd.com/papers/ijtsrd45066.pdf Paper URL: https://www.ijtsrd.com/mathemetics/applied-mathematics/45066/comparative-analysis-of-different-numerical-methods-for-the-solution-of-initial-value-problems-in-first-order-ordinary-differential-equations/vibahvari-tukaram-dhokrat
International Journal of Trend in Scientific Research and Development (IJTSRD)
Volume 5 Issue 5, July-August 2021 Available Online: www.ijtsrd.com e-ISSN: 2456 – 6470
@ IJTSRD | Unique Paper ID – IJTSRD45066 | Volume – 5 | Issue – 5 | Jul-Aug 2021
Page 1341
Comparative Analysis of Different Numerical Methods for the
Solution of Initial Value Problems in First Order
Ordinary Differential Equations
Vibahvari Tukaram Dhokrat
Assistant Professor, K.T.H.M. College, Nashik, Maharashtra, India
ABSTRACT
A mathematical equation which involves a function and its
derivatives is called a differential equation. We consider a real-life
situation, from this form a mathematical model, solve that model
using some mathematical concepts and take interpretation of solution.
It is a well-known and popular concept in mathematics because of its
massive application in real world problems. Differential equations are
one of the most important mathematical tools used in modeling
problems in Physics, Biology, Economics, Chemistry, Engineering
and medical Sciences. Differential equation can describe many
situations viz: exponential growth and de-cay, the population growth
of species, the change in investment return over time. We can solve
differential equations using classical as well as numerical methods, In
this paper we compare numerical methods of solving initial valued
first order ordinary differential equations namely Euler method,
Improved Euler method, Runge-Kutta method and their accuracy
level. We use here Scilab Software to obtain direct solution for these
methods.
KEYWORDS: Differential Equations, Accuracy, local Error, Global
Error Step-size
How to cite this paper: Vibahvari
Tukaram
Dhokrat
"Comparative
Analysis
of Different Numerical
Methods for the Solution of Initial Value
Problems in First Order Ordinary
Differential Equations" Published in
International
Journal of Trend in
Scientific Research
and Development
(ijtsrd), ISSN: 2456-
6470, Volume-5 |
Issue-5,
Augus