Some new numerical schemes for finding the solutions to nonlinear equations

Awais Gul Khan; Farah Ameen; Muhammad Uzair Awan; Kamsing Nonlaopon; Awais Gul Khan; Farah Ameen; Muhammad Uzair Awan; Kamsing Nonlaopon

doi:10.3934/math.20221024

AIMS Mathematics

2022, Volume 7, Issue 10: 18616-18631. doi: 10.3934/math.20221024

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Research article

Some new numerical schemes for finding the solutions to nonlinear equations

1.
Department of Mathematics, Government College University, Faisalabad 38023, Pakistan
2.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 22 June 2022 Revised: 31 July 2022 Accepted: 03 August 2022 Published: 19 August 2022
MSC : 49J40, 90C33

We introduce a sequence of third and fourth-order iterative schemes for finding the roots of nonlinear equations by using the decomposition technique and Simpson's one-third rule. We also discuss the convergence analysis of our suggested iterative schemes. With the help of different numerical examples, we demonstrate the validity, efficiency and implementation of our proposed schemes.
- convergence analysis,
- iterative method,
- decomposition technique,
- Simpson's one-third rule
Citation: Awais Gul Khan, Farah Ameen, Muhammad Uzair Awan, Kamsing Nonlaopon. Some new numerical schemes for finding the solutions to nonlinear equations[J]. AIMS Mathematics, 2022, 7(10): 18616-18631. doi: 10.3934/math.20221024

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Abstract

We introduce a sequence of third and fourth-order iterative schemes for finding the roots of nonlinear equations by using the decomposition technique and Simpson's one-third rule. We also discuss the convergence analysis of our suggested iterative schemes. With the help of different numerical examples, we demonstrate the validity, efficiency and implementation of our proposed schemes.

References

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