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A Modified Iterative Method for Solving Nonlinear Functional Equation

Arya Mohit

Arya Mohit

Department of Mathematics, School of Vocational Studies and Applied Sciences, Gautam Buddha UniversityGreater Noida, India
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Mohit, Arya
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Ujlayan Amit

Ujlayan Amit

Department of Mathematics, School of Vocational Studies and Applied Sciences, Gautam Buddha UniversityGreater Noida, India
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Amit, Ujlayan
  
20. Nov. 2020
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Online veröffentlicht: 20. Nov. 2020
Seitenbereich: 347 - 360
Eingereicht: 18. Okt. 2019
Akzeptiert: 14. Apr. 2020
DOI: https://doi.org/10.2478/amns.2020.2.00055
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© 2020 Arya Mohit et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

A comparison graph between AIM and exact solution.
A comparison graph between AIM and exact solution.

Fig. 2

Graph of the solution using AIM for the interval [0, 1).
Graph of the solution using AIM for the interval [0, 1).

Fig. 3

Graph of the solution using AIM for the interval [1, 1.1).
Graph of the solution using AIM for the interval [1, 1.1).

Fig. 4

Graph of the solution using AIM for the interval [1.1, 1.2).
Graph of the solution using AIM for the interval [1.1, 1.2).

Fig. 5

Graph of the solution using AIM in the interval [1.2, 1.3).
Graph of the solution using AIM in the interval [1.2, 1.3).

Fig. 6

Graph of the solution using MMIM for the interval [0, 2].
Graph of the solution using MMIM for the interval [0, 2].

Fig. 7

Comparison graph of the solution for the interval [0, 2] using AIM and exact solution.
Comparison graph of the solution for the interval [0, 2] using AIM and exact solution.

Fig. 8

Graph of the solution using AIM for the interval [0, 0.3).
Graph of the solution using AIM for the interval [0, 0.3).

Fig. 9

Graph of the solution using AIM in the interval [0.3, 0.4).
Graph of the solution using AIM in the interval [0.3, 0.4).

Fig. 10

Graph of the solution using MMIM for the interval [0, 2].
Graph of the solution using MMIM for the interval [0, 2].

Comparative study of AIM and MMIM

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
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