An Introduction of Numerical Methods for Unconstrained Nonlinear Equations

2018 ◽  
Author(s):  
Jerawan Chudoung Armstrong
Keyword(s):  
Numerical Methods ◽  
Nonlinear Equations

scholarly journals Shamanskii Method for Solving Parameterized Fuzzy Nonlinear Equations

2020 ◽  
Vol 11 (1) ◽  
pp. 24-29
Author(s):  
Sulaiman Mohammed Ibrahim ◽  
Mustafa Mamat ◽  
Puspa Liza Ghazali
Keyword(s):  
Numerical Methods ◽  
Nonlinear Equations ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Iteration Process ◽  
Benchmark Problems ◽  
Fuzzy Variables ◽  
Computationally Expensive ◽  
And Storage ◽  
Approximate Jacobian

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.

scholarly journals Solving Dual Fuzzy Nonlinear Equations via Shamanskii Method

2018 ◽  
Vol 7 (3.28) ◽  
pp. 89 ◽  
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. 

scholarly journals Numerical Solution of Nonlinear Equations in Maple

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.

scholarly journals Solution of nonlinear equations via Pade approximation. A Computer Algebra approach

2021 ◽  
Vol 66 (2) ◽  
pp. 321-328
Author(s):  
Radu T. Trimbitas
Keyword(s):  
Numerical Methods ◽  
Nonlinear Equations ◽  
Computer Algebra ◽  
Padé Approximation ◽  
High Order ◽  
Pade Approximation ◽  
Algebra Approach

"We generate automatically several high order numerical methods for the solution of nonlinear equations using Pad e approximation and Maple CAS."

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

2011 ◽  
Author(s):  
Alicia Cordero ◽  
Juan R. Torregrosa ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Nonlinear Equations ◽  
Nonlinear Equations And Systems

Numerical Methods for Solving Nonlinear Equations

2021 ◽  
pp. 121-145
Author(s):  
Narges Mohammadi ◽  
Shahram Mehdipour-Ataei ◽  
Maryam Mohammadi
Keyword(s):  
Numerical Methods ◽  
Nonlinear Equations

EFFECTS OF CASIMIR AND VAN DER WAALS FORCES ON THE PULL-IN INSTABILITY OF THE NONLINEAR MICRO AND NANO-BRIDGE GYROSCOPES

2014 ◽  
Vol 14 (02) ◽  
pp. 1350059 ◽  
Author(s):  
M. MOJAHEDI ◽  
M. T. AHMADIAN ◽  
K. FIROOZBAKHSH
Keyword(s):  
Numerical Methods ◽  
Nonlinear Equations ◽  
Proof Mass ◽  
Van Der Waals ◽  
Van Der Waals Forces ◽  
System Of Nonlinear Equations ◽  
Coriolis Forces ◽  
Homotopy Perturbation ◽  
Extended Hamilton’S Principle ◽  
Fringing Field

The influence of Casimir and van der Waals forces on the instability of vibratory micro and nano-bridge gyroscopes with proof mass attached to its midpoint is studied. The gyroscope subjected to the base rotation, Casimir and van der Waals attractions is actuated and detected by electrostatic methods. The system has two coupled bending motions actuated by the electrostatic and Coriolis forces. First a system of nonlinear equations for the flexural-flexural deflection of beam gyroscopes is derived using the extended Hamilton's principle. In modeling, the nonlinearities due to mid-plane stretching, electrostatic forces, including fringing field, Casimir and van der Waals attractions, are considered. The method of homotopy perturbation is used to solve the equations of equilibrium, with the solution validated by numerical methods. In addition, the effect of nondimensional parameters on the instability and deflection of the gyroscope is investigated. The data presented can be used in the design of vibratory micro/nano gyroscopes.

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