On iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation

被引：19

作者：

Shams, Mudassir ^{[1
]}

Rafiq, Naila ^{[2
]}

Kausar, Nasreen ^{[3
]}

Agarwal, Praveen ^{[4
,5
,6
]}

Park, Choonkil ^{[7
]}

Mir, Nazir Ahmad ^{[1
,2
]}

机构：

[1] Riphah Int Univ, Dept Math & Stat, I-14, Islamabad 44000, Pakistan

[2] NUML, Dept Math, Islamabad, Pakistan

[3] Yildiz Tech Univ, Fac Arts & Sci, Dept Math, TR-34210 Istanbul, Turkey

[4] Anand Int Coll Engn, Dept Math, Jaipur 303012, Rajasthan, India

[5] Harish Chandra Res Inst, Dept Math, Allahabad 211019, Uttar Pradesh, India

[6] Int Ctr Basic & Appl Sci, Jaipur 302029, Rajasthan, India

[7] Hanyang Univ, Res Inst Nat Sci, Dept Math, Seoul, South Korea

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2021年 / 2021卷 / 01期

关键词：

Single and all roots; Nonlinear system of equations; Iterative methods; Simultaneous methods; Basins of attraction; Boundary value problems; SIMULTANEOUS APPROXIMATION; NEWTON METHOD; CONVERGENCE; ORDER; ZEROS;

D O I：

10.1186/s13662-021-03636-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we construct a family of iterative methods for finding a single root of nonlinear equation and then generalize this family of iterative methods for determining all roots of nonlinear equations simultaneously. Further we extend this family of root estimating methods for solving a system of nonlinear equations. Convergence analysis shows that the order of convergence is 3 in case of the single root finding method as well as for the system of nonlinear equations and is 5 for simultaneous determination of all distinct and multiple roots of a nonlinear equation. The computational cost, basin of attraction, efficiency, log of residual and numerical test examples show that the newly constructed methods are more efficient as compared to the existing methods in literature.

引用

页数：18

共 40 条

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