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### Comparative Analysis of Different Numerical Methods for the Solution of Initial Value Problems in First Order Ordinary Differential Equations

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Comparative Analysis of Different Numerical Methods for the Solution of Initial Value Problems in First Order Ordinary Differential Equations

Vibahvari Tukaram Dhokrat

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, pp.1341-1343, URL: https://www.ijtsrd.com/papers/ijtsrd45066.pdf

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.

Differential Equations, Accuracy, local Error, Global Error Step-size

IJTSRD45066
Volume-5 | Issue-5, August 2021
1341-1343
IJTSRD | www.ijtsrd.com | E-ISSN 2456-6470