Regula Falsi Method for Solving Fuzzy Nonlinear Equation

Sulaiman, Ibrahim Mohammed; Mamat, Mustafa; Waziri, Mohammed Yusuf; Fadhilah, A.; Kamfa, Kamilu

doi:10.17654/ms100060873

Cited by 8 publications

(6 citation statements)

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“…Metode Regula Falsi (Regular False Method) atau Method of False Position adalah metode untuk menyelesaikan persamaan nonlinear yang sudah berusia ribuan tahun dengan menggabungkan dua buah metode, yaitu Metode Bisection dan Metode Secant (Abbasbandy & Liao, 2008). Metode ini menggunakan dua buah titik ( dan ) dengan nilai berbeda tanda (Sulaiman et al, 2016).…”

Section: Metode Regula Falsiunclassified

Comparison of the Number of Iterations of Roots of Non-Linear Equations in the Regula Falsi Method, Secant Method, and Bisection Method using Python

Yose Amelia,

Aryani,

Warsito

et al. 2024

FJST

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There are several methods for solving nonlinear equations, each method has a different number of iterations. This study aims to compare the number of iterations required by the Bisection, Regula Falsi, and Secant Method in finding the roots of an equation. These three methods were tested using two different equations in the Python programming language. From each equation in this study, Bisection Method requires thirteen and eighteen iterations, Regula Falsi Method requires nine and eight iterations, while Secant Method requires five iterations. From these three methods, Secant Method requires the fewest number of iterations, Regula Falsi Method requires a greater number of iterations than the Secant Method but less than the Bisection Method, and Bisection Method requires the highest number of iterations.

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Section: Metode Regula Falsiunclassified

Comparison of the Number of Iterations of Roots of Non-Linear Equations in the Regula Falsi Method, Secant Method, and Bisection Method using Python

Yose Amelia,

Aryani,

Warsito

et al. 2024

FJST

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“…(1) 𝑎𝑥 3 + 𝑏𝑥 2 + 𝑐𝑥 − 𝑑 = 𝑒 (2) 𝑝𝑥 2 + 𝑞𝑐𝑜𝑠(𝑥) = 𝑟 (3) 𝑐𝑥 2 + 𝑑 = 𝑒 Where 𝑎, 𝑏, 𝑐, 𝑑, 𝑒, 𝑝, 𝑞, 𝑎𝑛𝑑 𝑟 are intuitionistic fuzzy numbers. Numerous numerical algorithms have been developed for solving fuzzy nonlinear equations to overcome this drawback (Yang et al, 2008;Abbasbandy and Asady, 2004;Kajani et al, 2005;Sulaiman et al, 2016;Mohammed et al, 2020;Umar et al, 2020a;Sulaiman et al, 2021Sulaiman et al, , 2022b. However, only a few works of literature have investigated the performance of new iterative methods for solving equations whose coefficients are intuitionistic.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Hybrid Conjugate Gradient Algorithm for Solving Intuitionistic Fuzzy Nonlinear Equations

Omesa¹,

Sulaiman²,

Yusuf³

et al. 2023

BAS-SJKFU

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This paper presents an iterative algorithm for solving intuitionistic fuzzy nonlinear equations (IFNEs). The proposed method is based on the classical conjugate gradient (CG) search direction. An interesting feature of the new algorithm is that it considers problems based on the special triangular intuitionistic fuzzy number. For this purpose, intuitionistic fuzzy quantities are transformed into membership and non-membership parametric forms, and a line search procedure is employed to compute the step length. Preliminary results from numerical experiments are presented to demonstrate the performance of the method. It is observed that the proposed hybrid CG method is highly effective and promising. KEYWORDS Hybrid CG, intuitionistic fuzzy nonlinear equation, parametric form, step length, inexact line search

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“…However, the Chord technique also needs the computation of Jacobian either at first iteration or after few iterations. Recently, Regula Falsi method [7] was applied to solve FNE. This technique is the simplest and the most reliable one among bracketing approaches for finding the root of nonlinear equations.…”

Section: Introductionmentioning

confidence: 99%

Shamanskii Method for Solving Parameterized Fuzzy Nonlinear Equations

Sulaiman

Mamat

Ghazali

2020

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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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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Regula Falsi Method for Solving Fuzzy Nonlinear Equation

Cited by 8 publications

References 0 publications

Comparison of the Number of Iterations of Roots of Non-Linear Equations in the Regula Falsi Method, Secant Method, and Bisection Method using Python

Comparison of the Number of Iterations of Roots of Non-Linear Equations in the Regula Falsi Method, Secant Method, and Bisection Method using Python

An Efficient Hybrid Conjugate Gradient Algorithm for Solving Intuitionistic Fuzzy Nonlinear Equations

Shamanskii Method for Solving Parameterized Fuzzy Nonlinear Equations

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