Multiplicative Adams Bashforth–Moulton methods

Mısırlı, Emine; Gürefe, Yusuf

doi:10.1007/s11075-010-9437-2

Cited by 61 publications

(30 citation statements)

References 14 publications

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“…When an explicit Adams-Bashforth method is used as predictor and an implicit Adams-Moulton method is used as corrector, the approach is called Adams-Bashforth-Moulton. [27][28][29] The simplest Adams-Bashforth-Moulton method employs the explicit Euler method as predictor and the implicit trapezoidal rule as corrector. This methodology is called the Heun method 24 or one-step Adams-Bashforth-Moulton method.…”

Section: Adams-bashforth-moulton Methodsmentioning

confidence: 99%

“…Therefore, an explicit method is used to compute an approximate value of the following point (

{\overset{truê}{bold-italicx}}^{(k + 1)}

); then, the implicit method is run to correct it. When an explicit Adams‐Bashforth method is used as predictor and an implicit Adams‐Moulton method is used as corrector, the approach is called Adams‐Bashforth‐Moulton . The simplest Adams‐Bashforth‐Moulton method employs the explicit Euler method as predictor and the implicit trapezoidal rule as corrector.…”

Section: Proposed Lf Solvers Based On the Adams‐bashforth Formulamentioning

confidence: 99%

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Development of different load flow methods for solving large‐scale ill‐conditioned systems

Tostado‐Véliz

Kamel

2018

Int Trans Electr Energ Syst

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Summary In this paper, several methods are proposed to find the load flow (LF) solution of large‐scale ill‐conditioned systems. These methods are based on the Adams‐Bashforth formulation. With the use of the proposed methods, the convergence problems of the most popular LF methods are addressed especially when the flat initial guess point is considered. The proposed methods are validated using three ill‐conditioned systems: the modified IEEE 300‐bus system, the 3375‐bus Polish system, and a 13 659‐bus portion of the European transmission system. The obtained results prove that the proposed methods constitute a family of robust and efficient methods for the LF problem.

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Section: Adams-bashforth-moulton Methodsmentioning

confidence: 99%

“…Therefore, an explicit method is used to compute an approximate value of the following point (

{\overset{truê}{bold-italicx}}^{(k + 1)}

Section: Proposed Lf Solvers Based On the Adams‐bashforth Formulamentioning

confidence: 99%

Development of different load flow methods for solving large‐scale ill‐conditioned systems

Tostado‐Véliz

Kamel

2018

Int Trans Electr Energ Syst

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“…Since multiplicative differential equations are effectively used in many applications, their numerical solutions can not be ignored. Therefore, some important methods that deal with numerical solutions of multiplicative differential equations were introduced in Misirli and Gurefe and Riza et al, respectively.…”

Section: Introductionmentioning

confidence: 99%

Experimentally approved generalized model for circuit applications

Bilgehan¹,

Özyapıcı

Sensoy

2017

Circuit Theory & Apps

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Summary In this paper, generalized model based on the multiplicative least square method presented and showed that it is convenient to approximate observation in the electrical system analysis. The introduced model is exponential based and relies on parametric values. The advantage of the method is due to exponential derivation process within multiplicative calculus and has the flexibility to represent widely used functions such as Gaussian and exponentials. In spite of numerous results on the best fitting model, we study the robustness of the method by making direct comparisons with Matlab built‐in functions. The presented model is challenging because modern electrical circuits and systems are faced with different types of inputs that require near exact representation for accurate processing. Some real applications of exponential‐based data were selected to demonstrate the applicability and efficiency of the proposed representation.

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“…Also Ç akmak and Başar have constructed certain spaces of functions over the field of non-Newtonian complex numbers [7]. Also Misirli and Gurefe [13] have introduced multiplicative Adams Bashforth-Moulton methods for differential equations.…”

Section: Introductionmentioning

confidence: 99%

The Construction of Hilbert Spaces over the Non-Newtonian Field

Kadak

Efe

2014

International Journal of Analysis

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Although there are many excellent ways to present the principle of the classical calculus, the novel presentations probably lead most naturally to the development of the non-Newtonian calculi. In this paper we introduce vector spaces over real and complex nonNewtonian field with respect to the * -calculus which is a branch of non-Newtonian calculus. Also we give the definitions of real and complex inner product spaces and study Hilbert spaces which are special type of normed space and complete inner product spaces in the sense of * -calculus. Furthermore, as an example of Hilbert spaces, first we introduce the non-Cartesian plane which is a nonlinear model for plane Euclidean geometry. Secondly, we give Euclidean, unitary, and sequence spaces via corresponding norms which are induced by an inner product. Finally, by using the * -norm properties of complex structures, we examine CauchySchwarz and triangle inequalities.

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Multiplicative Adams Bashforth–Moulton methods

Cited by 61 publications

References 14 publications

Development of different load flow methods for solving large‐scale ill‐conditioned systems

Development of different load flow methods for solving large‐scale ill‐conditioned systems

Experimentally approved generalized model for circuit applications

The Construction of Hilbert Spaces over the Non-Newtonian Field

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