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 A New Approach for Solving Dual Fuzzy Nonlinear Equations Using Broyden's and Newton's Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
M. Y. Waziri ◽  
Z. A. Majid
Keyword(s):  
Nonlinear Equations ◽  
Newton's Method ◽  
Numerical Results ◽  
Parametric Form ◽  
New Approach ◽  
Broyden’S Method ◽  
Broyden's Method ◽  
Effectiveness And Efficiency ◽  
Initial Iteration ◽  
Newton's Methods

We present a new approach for solving dual fuzzy nonlinear equations. In this approach, we use Newton's method for initial iteration and Broyden's method for the rest of the iterations. The fuzzy coefficients are presented in parametric form. Numerical results on well-known benchmark fuzzy nonlinear equations are reported to authenticate the effectiveness and efficiency of the approach.

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 Chord Newton’s Method for Solving Fuzzy Nonlinear Equations

2019 ◽  
Vol 7 (1) ◽  
pp. 16
Author(s):  
Aliyu Usman Moyi
Keyword(s):  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Jacobian Matrix ◽  
Numerical Results ◽  
Parametric Form ◽  
New Approach ◽  
Effectiveness And Efficiency

In this paper, we present a new approach for solving fuzzy nonlinear equations. Our approach requires to  compute the Jacobian matrix once throughout the iterations unlike some Newton’s-like methods which needs to compute the Jacobian matrix in every iterations. The fuzzy coefficients are presented in parametric form. Numerical results on well-known benchmarks fuzzy nonlinear equations are reported to authenticate the effectiveness and efficiency of the approach.

scholarly journals SOLVING DUAL FUZZY NONLINEAR EQUATIONS VIA MODIFIED STIRLING’S METHOD

2019 ◽  
Vol 4 (14) ◽  
pp. 84-91
Author(s):  
A. O Umar ◽  
M Mamat ◽  
M.Y Waziri
Keyword(s):  
Fixed Point ◽  
Nonlinear Equations ◽  
Unique Fixed Point ◽  
Numerical Results ◽  
Benchmark Problems ◽  
Parametric Form ◽  
Root Finding ◽  
Root Finding Method ◽  
Finding Method

Stirling’s method is a root-finding method designed to approximate a locally unique fixed point and cannot be used to solve fuzzy nonlinear equations. In this paper, we present a modified Stirling’s method for solving dual fuzzy nonlinear equations. The fuzzy coefficient is presented in parametric form. Numerical results on some benchmark problems indicate that the proposed method is efficient.

Symplectic Irregular Interpolation Algorithms for Optimal Control Problems

2015 ◽  
Vol 12 (06) ◽  
pp. 1550040 ◽  
Author(s):  
Mingwu Li ◽  
Haijun Peng ◽  
Zhigang Wu
Keyword(s):  
Optimal Control ◽  
Numerical Methods ◽  
Numerical Method ◽  
Computational Efficiency ◽  
Optimal Control Problems ◽  
Numerical Results ◽  
Control Problems ◽  
Collocation Points ◽  
Comparison Results ◽  
Made In

Symplectic numerical methods for optimal control problems with irregular interpolation schemes are developed and the comparisons between irregular interpolation schemes and equidistant scheme are made in this paper. The irregular interpolation points, which are the collocation points usually adopted by pseudospectral (PS) methods, such as Legendre–Gauss, Legendre–Gauss–Radau, Legendre–Gauss–Lobatto and Chebyshev–Gauss–Lobatto points, are taken into consideration in this study. The symplectic numerical method with irregular points is proposed firstly. Then, several examples with different complexities highlight the differences in performance between different kinds of interpolation schemes. The numerical results show that the convergence of the present symplectic numerical methods can be obtained by increasing the number of sub-intervals or the number of interpolation points. Moreover, the comparison results show that the convergence of the symplectic numerical methods are generally independent on the type of interpolation points and the computational efficiency is not sensitive to the choice of interpolation points in general. Thus, the symplectic numerical methods with different interpolation schemes have obvious difference with the PS methods.

Impulse formulation of the Euler equations: general properties and numerical methods

1999 ◽  
Vol 391 ◽  
pp. 189-209 ◽  
Author(s):  
GIOVANNI RUSSO ◽  
PETER SMEREKA
Keyword(s):  
Numerical Methods ◽  
Numerical Method ◽  
Gauge Transformation ◽  
Euler Equations ◽  
Numerical Scheme ◽  
Numerical Results ◽  
Gauge Freedom ◽  
General Properties ◽  
Three Space ◽  
Incompressible Euler

The gauge freedom of the incompressible Euler equations is explored. We present various forms of the Euler equations written in terms of the impulse density. It is shown that these various forms are related by a gauge transformation. We devise a numerical method to solve the impulse form of the Euler equations in a variety of gauges. The numerical scheme is implemented both in two and three space dimensions. Numerical results are presented showing that the impulse density tends to concentrate on sheets.

scholarly journals Problems and solutions by the application of Julia set theory to one-dot and multi-dots numerical methods

2001 ◽  
Vol 28 (9) ◽  
pp. 545-548
Author(s):  
Anna Tomova
Keyword(s):  
Numerical Methods ◽  
Numerical Method ◽  
Nonlinear Equations ◽  
Set Theory ◽  
Julia Set ◽  
Time Algorithm ◽  
Escape Time ◽  
Special Cases ◽  
Problems And Solutions ◽  
The One

In 1977 Hubbard developed the ideas of Cayley (1879) and solved in particular the Newton-Fourier imaginary problem. We solve the Newton-Fourier and the Chebyshev-Fourier imaginary problems completely. It is known that the application of Julia set theory is possible to the one-dot numerical method like the Newton's method for computing solution of the nonlinear equations. The secants method is the two-dots numerical method and the application of Julia set theory to it is not demonstrated. Previously we have defined two one-dot combinations: the Newton's-secants and the Chebyshev's-secants methods and have used the escape time algorithm to analyse the application of Julia set theory to these two combinations in some special cases. We consider and solve the Newton's-secants and Tchebicheff's-secants imaginary problems completely.

scholarly journals Numerical methods for solving the multi-term time-fractional wave-diffusion equation

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Fawang Liu ◽  
Mark Meerschaert ◽  
Robert McGough ◽  
Pinghui Zhuang ◽  
Qingxia Liu
Keyword(s):  
Numerical Methods ◽  
Theoretical Analysis ◽  
Diffusion Equation ◽  
Fractional Derivatives ◽  
Fractional Laplacian ◽  
Numerical Results ◽  
Diffusion Equations ◽  
Time Space ◽  
Methods And Techniques ◽  
Wave Diffusion

AbstractIn this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

Observations Regarding Numerical Results Obtained by the Floquet-Method

2013 ◽  
Author(s):  
Till J. Kniffka ◽  
Horst Ecker
Keyword(s):  
Numerical Methods ◽  
Monodromy Matrix ◽  
Mathieu Equation ◽  
Numerical Results ◽  
The Other ◽  
Benchmark Problem ◽  
Stability Studies ◽  
Floquet Method ◽  
System Equations ◽  
Time Periodic

Stability studies of parametrically excited systems are frequently carried out by numerical methods. Especially for LTP-systems, several such methods are known and in practical use. This study investigates and compares two methods that are both based on Floquet’s theorem. As an introductary benchmark problem a 1-dof system is employed, which is basically a mechanical representation of the damped Mathieu-equation. The second problem to be studied in this contribution is a time-periodic 2-dof vibrational system. The system equations are transformed into a modal representation to facilitate the application and interpretation of the results obtained by different methods. Both numerical methods are similar in the sense that a monodromy matrix for the LTP-system is calculated numerically. However, one method uses the period of the parametric excitation as the interval for establishing that matrix. The other method is based on the period of the solution, which is not known exactly. Numerical results are computed by both methods and compared in order to work out how they can be applied efficiently.

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