Novel Three Order Methods for Solving a System of Nonlinear Equations

Khirallah, Mustafa Q.; Hafiz, M.A.

doi:10.18052/www.scipress.com/bmsa.2.1

Cited by 10 publications

(9 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Step 2: We can find the Taylor series of 𝐹(𝑦 𝑛 ) and 𝐹 ′ (𝑤 𝑟 ) in step 2 of Equation (7), where r = 1, 2, 3, and 4…”

Section: Proofmentioning

confidence: 99%

“…It means the algorithm can produce the solution faster. Several modifications of algorithms have been introduced and investigated [1][2][3][4][5][6][7]. However, discovering the other high order algorithm is highly possible.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, Darvishi et al [3][4] investigated and proposed two new methods: Newton-like 3 rd -order of convergence method and super cubic iterative approach to solve nonlinear equation system. Khirallah and Hafiz developed 3 rd -order Newton-family and Jarrat methods to solve non-linear equation systems in 2012 [7], called KHM methods.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

High Order Three-Steps Newton Raphson-like Schemes for Solving Nonlinear Equation Systems

Fatahillah¹,

Arif²,

Hidayat³

et al. 2022

Advances in Computer Science Research

View full text Add to dashboard Cite

This study proposes several new 3-steps schemes based on the Newton-Raphson method for solving non-linear equation systems. The proposed schemes are analysed and formulated based on the Newton-Raphson method and the Newtoncotes open form numerical integration method. In general, the schemes can be considered as a predictor and corrector principles. In the first and the third steps, the Newton-Raphson method is applied. Furthermore, Newton-cotes Open Form numerical integration modification is operated in the second step of the proposed schemes. The convergence analysis of the proposed schemes is given. It shows that the proposed scheme provides the 8 th order of convergence. The performance of the proposed schemes is compared and assessed with several numerical examples.

show abstract

“…Step 2: We can find the Taylor series of 𝐹(𝑦 𝑛 ) and 𝐹 ′ (𝑤 𝑟 ) in step 2 of Equation (7), where r = 1, 2, 3, and 4…”

Section: Proofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

High Order Three-Steps Newton Raphson-like Schemes for Solving Nonlinear Equation Systems

Fatahillah¹,

Arif²,

Hidayat³

et al. 2022

Advances in Computer Science Research

View full text Add to dashboard Cite

show abstract

“…The idea used in developing quadrature based iterative methods is the approximation of the integral in the Taylor expansion of vector function using quadrature formulas, [26] [27]. The quadrature based iterative functions are implicit-type, [19] [20] [21] [28] [29]. To implement the implicit iterative formula derived via quadrature formula, the predictor and corrector technique is utilized with the Newton method used often as predictor and the iterative function derived from quadrature formula as corrector.…”

Section: Introductionmentioning

confidence: 99%

Multistep Quadrature Based Methods for Nonlinear System of Equations with Singular Jacobian

Oghovese¹,

Muka²

2019

JAMP

View full text Add to dashboard Cite

Methods for the approximation of solution of nonlinear system of equations often fail when the Jacobians of the systems are singular at iteration points. In this paper, multi-step families of quadrature based iterative methods for approximating the solution of nonlinear system of equations with singular Jacobian are developed using decomposition technique. The methods proposed in this study are of convergence order 4 ρ ≤ , and require only the evaluation of first-order Frechet derivative per iteration. The approximate solutions generated by the proposed iterative methods in this paper compared with some existing contemporary methods in literature, show that methods developed herein are efficient and adequate in approximating the solution of nonlinear system of equations whose Jacobians are singular and non-singular at iteration points.

show abstract

“…In recent years, several iterative methods have been used to solve nonlinear equations and systems of nonlinear equations. In order to improve the order of convergence, a few two-step variants of Newton's methods with cubic convergence have been proposed in some literature [3]- [11] and references therein for solving systems of nonlinear equations. S. We erakoon and T. Fernando [5] using the Newton theorem ( ) ( )…”

Section: Introductionmentioning

confidence: 99%

Gauss-Legendre Iterative Methods and Their Applications on Nonlinear Systems and BVP-ODEs

Liu¹,

Sun²

2016

JAMP

View full text Add to dashboard Cite

In this paper, a group of Gauss-Legendre iterative methods with cubic convergence for solving nonlinear systems are proposed. We construct the iterative schemes based on Gauss-Legendre quadrature formula. The cubic convergence and error equation are proved theoretically, and demonstrated numerically. Several numerical examples for solving the system of nonlinear equations and boundary-value problems of nonlinear ordinary differential equations (ODEs) are provided to illustrate the efficiency and performance of the suggested iterative methods.

show abstract

Novel Three Order Methods for Solving a System of Nonlinear Equations

Cited by 10 publications

References 19 publications

High Order Three-Steps Newton Raphson-like Schemes for Solving Nonlinear Equation Systems

High Order Three-Steps Newton Raphson-like Schemes for Solving Nonlinear Equation Systems

Multistep Quadrature Based Methods for Nonlinear System of Equations with Singular Jacobian

Gauss-Legendre Iterative Methods and Their Applications on Nonlinear Systems and BVP-ODEs

Contact Info

Product

Resources

About