A new method based on Muller’s algorithm for solving nonlinear equations has been developed. The classic Muller’s method is based on an interpolating polynomial built on the last three points of an ...iterative sequence. Unfortunately, Muller’s method is not globally convergent. In order to ensure the global convergence a bracketing is introduced. The proposed method does not require the use of a derivative of the function and is more rapidly convergent than a classical regula falsi method. The method is good alternative to other bracketing methods.
A new and improved version of Mullcr method and Bisection method with global and asymptotic superlinear convergence for finding a simple root
x* of a nonlinear equation
f
(
x)
=
0 in the interval
a,
...b is proposed in this paper. The new iteration procedure combines Muller method with Bisection method to generate simultaneously two sequences {
x
n
} which goes to
x* and {
a
n
,
b
n
} which encloses
x*. The global and superlinear convergence for the both sequences {
x
n
} and {
b
n
−
a
n
} are analyzed. The asymptotic efficiency index of the improved Muller method and Bisection method for the both sequences {
x
n
} and {
b
n
−
a
n
} proves to be 1.84 approximately on certain conditions, in the sense of Ostrowski. As a result, the new and improved version of Muller method and Bisection method preserve their respective nice property and remove their respective defect. The new version has been tested on a series of elementary functions. The numerical results show that the new version of Muller method and Bisection method proposed in this paper is more effective compared with the traditional version for solving nonlinear equations. For the computation of multiple zeros a effective strategy is discussed.
This paper presents the Improved Pre-prepared Power Demand (IPPD) table and Muller’s method as a means of solving the Profit Based Unit Commitment (PBUC) problem. In a deregulated environment, ...generation companies (GENCOs) schedule their generators to maximize profits rather than to satisfy power demand. The PBUC problem is solved by the proposed approach in two stages. Initially, information concerning committed units is obtained by the IPPD table and then the subproblem of Economic Dispatch (ED) is solved using Muller’s method. The proposed approach has been tested on a power system with 3 and 10 generating units. Simulation results of the proposed approach have been compared with existing methods and also with traditional unit commitment. It is observed from the simulation results that the proposed algorithm provides maximum profit with less computational time compared to existing methods. KCI Citation Count: 12
The small-signal analysis of an oscillator relative to a periodic steady-state (PSS) would generate periodic time-varying characteristic poles. Analyzing periodic root-loci can provide useful design ...information, which is not available from the existing circuit simulation tools. Although the numerical QZ algorithm can be used to generate periodic root-loci, this paper proposes an alternative symbolic computation method for repeated pole computation. It is demonstrated that the Muller algorithm can be used for finding the dominant periodic roots of a characteristic polynomial with periodic coefficients, whose efficiency is superior to the matrix-based numerical QZ method. Other advantages of symbolic root-locus analysis also are explored by applying the proposed method to the analysis of two oscillator circuits.
A standard method of reducing sugars determination using Fehling-Muller reagent has been modified and applied to control the presence of sucrose in white dry wine that can be considered as an ...indication of its falsification. Natural dry wine should not contain any significant amounts of sucrose since its content in regular grape is below 0.9 wt % and it would be fermented almost completely in the course of wine maturing and manufacturing. However, some sucrose can be addedby fraudulent producers to the source wine materials in order to accelerate its fermentation. This results in a higher content of residual sucrose in dry wine that can exceed its maximum permissible level of 4 g/l. The modified method of the reducing sugars determination has shown good durability and reproducibility and can be used to determine the residual sucrose concentration above 1.33 g/l. However, excessive sulfites and other reducing preservatives present in some wines (especially in the low-grade samples) can distort the analysis results and should be removed in advance. Potentially, this method can also be applied to analyze wine blending samples and to control their affinity by the ratio between reducing and non-reducing sugars contents.
This paper proposes a new methodology for solving Unit Commitment (UC) problem. In the proposed approach, Improved Pre-prepared Power Demand (IPPD) table solves the UC problem and then the Muller ...method solves the Economic Dispatch (ED) sub-problem. The proposed method has been tested on 3–, 10–, 38– and 40–100 units. Comparison of the simulation results of the proposed method with the results of previous published methods shows that the proposed method provides better solution with less computational time.
Several methods based on combinations of bisection, regula falsi, and parabolic interpolation has been developed. An interval bracketing ensures the global convergence while the combination with the ...parabolic interpolation increases the speed of the convergence. The proposed methods have been tested on a series of examples published in the literature and show good results.
We present an improved convergence analysis of Müller's method for solving nonlinear equation under conditions that the divided differences of order one of the involved function satisfy the Lipschitz ...conditions. Our result improves the earlier work in literature. Numerical examples are presented to illustrate the theoretical results.
The problem of solving the dispersion relations for waves in guiding electrodynamic structures on the complex planes of wavenumbers is considered. A method combining the positive features of the ...Muller method and the phase variation method based on the argument principle is proposed. The implementation of the method is described. For estimating the correctness of the solutions obtained, a new approach employing the convergence to zero of the period-averaged power flux of complex waves is suggested.
Spherical cap harmonic (SCH) theory has been widely used to format regional model of fields that can be expressed as the gradient of a scalar potential. The functions of this method consist of ...trigonometric functions and associated Legendre functions with integral-order but non-integral degree. Evidently, the constructing and computing of Legendre functions are the core content of the spherical cap functions. In this paper,the approximated calculation method of the normalized association Legendre functions with non-integral degree is introduced and an analysis of the entire order of associated non-Legendre function calculation is presented. Besides, we use the Muller method to search out for all intrinsic values. The results showed that the highest order of spherical harmonic function for constructing regional model of fields is limited, thus high-resolution spherical harmonic structure of local gravity field need to be improved.
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