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Published in:

Volume 5 Issue 4
April-2018
eISSN: 2349-5162

Unique Identifier

JETIR1804028

Page Number

135-142

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Title

A Study on Numerical Solutions of Initial Value Problems (IVP) for Ordinary Differential Equations (ODE) with 4th-Order of Taylor’s Method and 4th-Order of RK Methods Using Matlab

ISSN

2349-5162

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"A Study on Numerical Solutions of Initial Value Problems (IVP) for Ordinary Differential Equations (ODE) with 4th-Order of Taylor’s Method and 4th-Order of RK Methods Using Matlab", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.5, Issue 4, page no.135-142, April-2018, Available :http://www.jetir.org/papers/JETIR1804028.pdf

Abstract

So far , This paper mainly presents fourth-order of Taylor’s Method and fourth-order of Runge-kutta’s method for solving initial value problems (IVP) for ordinary differential equations (ODE). The three methods are quite efficient and practically well suited for solving these problems. In order to verify the accuracy, we compare numerical solutions with the exact solutions in Matlab. The numerical solutions are in good agreement with the exact solutions. Numerical comparisons between Fourth-order Taylor’s Method and fourth-order of Runge-kutta’s method have been compare. We also compare the performance and the computational effort of such methods. In order to achieve higher accuracy in the solution, the step size needs to be very small. Finally we investigate and compute the errors of the three proposed methods for different step sizes to examine superiority.

Key Words

Initial Value Problem (IVP), Fourth-Order of Taylor’s method , Fourth-Order of Runge Kutta Method, Error Analysis, MATLAB

Cite This Article

"A Study on Numerical Solutions of Initial Value Problems (IVP) for Ordinary Differential Equations (ODE) with 4th-Order of Taylor’s Method and 4th-Order of RK Methods Using Matlab", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.5, Issue 4, page no. pp135-142, April-2018, Available at : http://www.jetir.org/papers/JETIR1804028.pdf

Publication Details

Published Paper ID: JETIR1804028
Registration ID: 180946
Published In: Volume 5 | Issue 4 | Year April-2018
DOI (Digital Object Identifier): http://doi.one/10.1729/IJCRT.17367
Page No: 135-142
ISSN Number: 2349-5162

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Cite This Article

"A Study on Numerical Solutions of Initial Value Problems (IVP) for Ordinary Differential Equations (ODE) with 4th-Order of Taylor’s Method and 4th-Order of RK Methods Using Matlab", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.5, Issue 4, page no. pp135-142, April-2018, Available at : http://www.jetir.org/papers/JETIR1804028.pdf




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