scholarly journals A New Application of Gauss Quadrature Method for Solving Systems of Nonlinear Equations

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 432
Author(s):  
Hari M. Srivastava ◽  
Javed Iqbal ◽  
Muhammad Arif ◽  
Alamgir Khan ◽  
Yusif S. Gasimov ◽  
...  
Keyword(s):  
Nonlinear Equations ◽  
Nonlinear Boundary ◽  
Quadrature Rule ◽  
Gauss Quadrature ◽  
New Method ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Numerical Comparison ◽  
Nonlinear Boundary Value Problems ◽  
Gauss Quadrature Rule

In this paper, we introduce a new three-step Newton method for solving a system of nonlinear equations. This new method based on Gauss quadrature rule has sixth order of convergence (with n=3). The proposed method solves nonlinear boundary-value problems and integral equations in few iterations with good accuracy. Numerical comparison shows that the new method is remarkably effective for solving systems of nonlinear equations.

scholarly journals En enhanced matrix-free method via double step length approach for solving systems of nonlinear equations

2017 ◽  
Vol 6 (4) ◽  
pp. 147 ◽  
Author(s):  
Abubakar Sani Halilu ◽  
H. Abdullahi ◽  
Mohammed Yusuf Waziri
Keyword(s):  
Nonlinear Equations ◽  
Large Scale ◽  
Step Length ◽  
Systems Of Nonlinear Equations ◽  
Test Problems ◽  
System Of Nonlinear Equations ◽  
Numerical Comparison ◽  
Inexact Line Search ◽  
Derivative Free ◽  
Variant Method

A variant method for solving system of nonlinear equations is presented. This method use the special form of iteration with two step length parameters, we suggest a derivative-free method without computing the Jacobian via acceleration parameter as well as inexact line search procedure. The proposed method is proven to be globally convergent under mild condition. The preliminary numerical comparison reported in this paper using a large scale benchmark test problems show that the proposed method is practically quite effective.

scholarly journals Rational Transformations for Evaluating Singular Integrals by the Gauss Quadrature Rule

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 677
Author(s):  
Beong In Yun
Keyword(s):  
Numerical Evaluation ◽  
Singular Integrals ◽  
Quadrature Rule ◽  
Transformation Method ◽  
Gauss Quadrature ◽  
Cauchy Principal ◽  
Weakly Singular ◽  
Principal Value ◽  
Transformation Methods ◽  
Gauss Quadrature Rule

In this work we introduce new rational transformations which are available for numerical evaluation of weakly singular integrals and Cauchy principal value integrals. The proposed rational transformations include parameters playing an important role in accelerating the accuracy of the Gauss quadrature rule used for the singular integrals. Results of some selected numerical examples show the efficiency of the proposed transformation method compared with some existing transformation methods.

scholarly journals On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
H. Montazeri ◽  
F. Soleymani ◽  
S. Shateyi ◽  
S. S. Motsa
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Efficiency Index ◽  
The Other ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Numerical Tests ◽  
Programming Package ◽  
New Iterative Method

We consider a system of nonlinear equationsF(x)=0. A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.

Motion control of the two joint planar robotic manipulators through accelerated Dai–Liao method for solving system of nonlinear equations

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abubakar Sani Halilu ◽  
Arunava Majumder ◽  
Mohammed Yusuf Waziri ◽  
Kabiru Ahmed ◽  
Aliyu Muhammed Awwal
Keyword(s):  
Motion Control ◽  
Nonlinear Equations ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Robotic Manipulators ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Content Type ◽  
Conjugate Gradient Algorithms

PurposeThe purpose of this research is to propose a new choice of nonnegative parameter t in Dai–Liao conjugate gradient method.Design/methodology/approachConjugate gradient algorithms are used to solve both constrained monotone and general systems of nonlinear equations. This is made possible by combining the conjugate gradient method with the Newton method approach via acceleration parameter in order to present a derivative-free method.FindingsA conjugate gradient method is presented by proposing a new Dai–Liao nonnegative parameter. Furthermore the proposed method is successfully applied to handle the application in motion control of the two joint planar robotic manipulators.Originality/valueThe proposed algorithm is a new approach that will not either submitted or publish somewhere.

scholarly journals Two-step Ulm-type method for solving nonlinear operator equations

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 723-730
Author(s):  
Wei Ma ◽  
Liuqing Hua
Keyword(s):  
Convergence Rate ◽  
Nonlinear Equations ◽  
Nonlinear Operator ◽  
New Method ◽  
Systems Of Nonlinear Equations ◽  
Operator Equations ◽  
Type Method ◽  
Jacobian Matrices ◽  
Nonlinear Operator Equations

In this paper, we present a two-step Ulm-type method to solve systems of nonlinear equations without computing Jacobian matrices and solving Jacobian equations. we prove that the two-step Ulm-type method converges locally to the solution with R-convergence rate 3. Numerical implementations demonstrate the effectiveness of the new method.

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