<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>An iterative method (AIM) is one of the numerical method, which is easy to apply and very time convenient for solving nonlinear differential equations. However, if we want to work in a large interval, sometimes it may be difficult to apply AIM. Therefore, a multistage AIM named Multistage Modified Iterative Method (MMIM) is introduced in this article to work in a large computational interval. The applicability of MMIM for increasing the solution domain of the given problems is construed in this article. Some problems are solved numerically using MMIM, which provides a better result in the extended interval as compared to AIM. Comparison tables and some graphs are included to demonstrate the results.</p>
</abstract>

An iterative method (AIM) is one of the numerical method, which is easy to apply and very time convenient for solving nonlinear differential equations. However, if we want to work in a large interval, sometimes it may be difficult to apply AIM. Therefore, a multistage AIM named Multistage Modified Iterative Method (MMIM) is introduced in this article to work in a large computational interval. The applicability of MMIM for increasing the solution domain of the given problems is construed in this article. Some problems are solved numerically using MMIM, which provides a better result in the extended interval as compared to AIM. Comparison tables and some graphs are included to demonstrate the results.

A Modified Iterative Method for Solving Nonlinear Functional Equation

Department of Mathematics, School of Vocational Studies and Applied Sciences

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"A Modified Iterative Method for Solving Nonlinear Functional Equation"}

An iterative method (AIM) is one of the numerical method, which is easy to apply and very time convenient for solving nonlinear differential equations....

t	Exact value	Absolute error (AIM)	Absolute error (MMIM)
0.4	1.4	2.878×10⁻³	4.475×10⁻⁶
0.8	1.8	0.147	1.260×10⁻⁵
1.2	2.2	1.203	2.865×10⁻⁵
1.6	2.6	3.393	5.664×10⁻⁵
2.0	3.0	5.401	1.012×10⁻⁴

A Modified Iterative Method for Solving Nonlinear Functional Equation

Publié en ligne: 20 nov. 2020

Pages: 347 - 360

Reçu: 18 oct. 2019

Accepté: 14 avr. 2020

DOI: https://doi.org/10.2478/amns.2020.2.00055

Mots clés
an iterative method, multistage modified iterative method, nonlinear integral equations, ordinary differential equations

© 2020 Arya Mohit et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Comparative study of AIM and MMIM

A Modified Iterative Method for Solving Nonlinear Functional Equation

Publié en ligne: 20 nov. 2020

Pages: 347 - 360

Reçu: 18 oct. 2019

Accepté: 14 avr. 2020

DOI: https://doi.org/10.2478/amns.2020.2.00055

Mots clésan iterative method, multistage modified iterative method, nonlinear integral equations, ordinary differential equations

© 2020 Arya Mohit et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Comparative study of AIM and MMIM

Mots clés
an iterative method, multistage modified iterative method, nonlinear integral equations, ordinary differential equations