Preface of the “Advances in Numerical Methods for Solving Nonlinear Equations and Systems”

One of the most significant problems in fuzzy set theory is solving fuzzy nonlinear equations. Numerous researches have been done on numerical methods for solving these problems, but numerical investigation indicates that most of the methods are computationally expensive due to computing and storage of Jacobian or approximate Jacobian at every iteration. This paper presents the Shamanskii algorithm, a variant of Newton method for solving nonlinear equation with fuzzy variables. The algorithm begins with Newton’s step at first iteration, followed by several Chord steps thereby reducing the high cost of Jacobian or approximate Jacobian evaluation during the iteration process. The fuzzy coe?cients of the nonlinear systems are parameterized before applying the proposed algorithm to obtain their solutions. Preliminary results of some benchmark problems and comparisons with existing methods show that the proposed method is promising.

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Solving Dual Fuzzy Nonlinear Equations via Shamanskii Method

International Journal of Engineering & Technology ◽

10.14419/ijet.v7i3.28.20974 ◽

2018 ◽

Vol 7 (3.28) ◽

pp. 89 ◽

Cited By ~ 1

Author(s):

Ibrahim Mohammed Sulaiman ◽

Mustafa Mamat ◽

Nurnadiah Zamri ◽

Puspa Liza Ghazali

Keyword(s):

Numerical Methods ◽

Numerical Method ◽

Nonlinear Equations ◽

Computational Cost ◽

Numerical Results ◽

Parametric Form ◽

Solution Point ◽

New Ideas

New ideas on numerical methods for solving fuzzy nonlinear equations have spread quickly across the globe. However, most of the methods available are based on Newton’s approach whose performance is impaired by either discontinuity or singularity of the Jacobian at the solution point. Also, the study of dual fuzzy nonlinear equations is yet to be explored by many researchers. Thus, in this paper, a numerical method to investigate the solution of dual fuzzy nonlinear equations is proposed. This method reduces the computational cost of Jacobian evaluation at every iteration. The fuzzy coeﬃcients are presented in its parametric form. Numerical results obtained have shown that the proposed method is efficient.

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Nonlinear equations and systems in several space variables

Journal of Differential Equations ◽

10.1016/0022-0396(83)90060-8 ◽

1983 ◽

Vol 48 (1) ◽

pp. 71-94

Author(s):

Gunduz Caginalp

Keyword(s):

Nonlinear Equations ◽

Nonlinear Equations And Systems

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Exact Solutions to Nonlinear Equations and Systems of Equations of General Form in Mathematical Physics

10.1063/1.3030831 ◽

2008 ◽

Cited By ~ 2

Author(s):

A. D. Polyanin ◽

A. I. Zhurov ◽

E. A. Vyazmina ◽

Michail D. Todorov

Keyword(s):

Exact Solutions ◽

Nonlinear Equations ◽

Mathematical Physics ◽

Systems Of Equations ◽

Nonlinear Equations And Systems

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Numerical Solution of Nonlinear Equations in Maple

International Journal for Research in Applied Sciences and Biotechnology ◽

10.31033/ijrasb.8.4.6 ◽

2021 ◽

Vol 8 (4) ◽

Author(s):

Qani Yalda

Keyword(s):

Numerical Methods ◽

Numerical Solution ◽

Numerical Method ◽

Nonlinear Equations ◽

Secant Method ◽

Bisection Method ◽

Real Roots ◽

Newton Raphson ◽

Root Analysis ◽

Raphson Method

The main purpose of this paper is to obtain the real roots of an expression using the Numerical method, bisection method, Newton's method and secant method. Root analysis is calculated using specific, precise starting points and numerical methods and is represented by Maple. In this research, we used Maple software to analyze the roots of nonlinear equations by special methods, and by showing geometric diagrams, we examined the relevant examples. In this process, the Newton-Raphson method, the algorithm for root access, is fully illustrated by Maple. Also, the secant method and the bisection method were demonstrated by Maple by solving examples and drawing graphs related to each method.

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