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Article
Publication date: 14 September 2012

Yiğit Aksoy, Mehmet Pakdemirli, Saeid Abbasbandy and Hakan Boyacı

The purpose of this paper is to apply, for the first time, the authors' newly developed perturbation iteration method to heat transfer problems. The effectiveness of the new…

Abstract

Purpose

The purpose of this paper is to apply, for the first time, the authors' newly developed perturbation iteration method to heat transfer problems. The effectiveness of the new method in nonlinear heat transfer problems will be tested.

Design/methodology/approach

Nonlinear heat transfer problems are solved by perturbation iteration method. They are also solved by the well‐known technique variational iteration method in the literature.

Findings

It is found that perturbation iteration solutions converge faster to the numerical solutions. More accurate results can be achieved with this new method for nonlinear heat transfer problems.

Research limitations/implications

A few iterations are actually sufficient. Further iterations need symbolic packages to calculate the solutions.

Practical implications

This new technique can practically be applied to many heat and flow problems.

Originality/value

The new perturbation iteration technique is successfully implemented to nonlinear heat transfer problems. Results show good agreement with the direct numerical simulations and the method performs better than the existing variational iteration method.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 22 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 3 May 2016

Mustafa Turkyilmazoglu

In an earlier paper (Turkyilmazoglu, 2011a), the author introduced a new optimal variational iteration method. The idea was to insert a parameter into the classical variational…

Abstract

Purpose

In an earlier paper (Turkyilmazoglu, 2011a), the author introduced a new optimal variational iteration method. The idea was to insert a parameter into the classical variational iteration formula in an aim to prevent divergence or to accelerate the slow convergence property of the classical approach. The purpose of this paper is to approve the superiority of the proposed method over the traditional one on several physical problems treated before by the classical variational iteration method.

Design/methodology/approach

A sufficient condition theorem with an upper bound for the error is also presented to further justify the convergence of the new variational iteration method.

Findings

The optimal variational iteration method is found to be useful for heat and fluid flow problems.

Originality/value

The optimal variational iteration method is shown to be convergent under sufficient conditions. A novel approach to obtain the optimal convergence parameter is introduced.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 3/4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 March 1987

Richard J. Schmidt and Robert H. Dodds

The computational efficiency of subspace iteration is addressed relative to the data structures adopted for the very large and generally sparse coefficient matrices. The frequent…

Abstract

The computational efficiency of subspace iteration is addressed relative to the data structures adopted for the very large and generally sparse coefficient matrices. The frequent triangulations and matrix multiplications demand that access to the terms in the coefficient matrices be unbiased. Reliance on virtual memory (paging) operating systems with no special considerations for localized data access is not adequate. Specific data structures must be designed that accommodate the needs of the numerical algorithm yet eliminate unnecessary paging. An implementation of the subspace iteration method using hypermatrix data structures is presented. Use of hypermatrices is shown to provide unbiased and localized data access. The various modifications to the conventional formulation are described and an example problem illustrates the potential benefits of the hypermatrix formulation. Possibilities for adapting hypermatrix data structures to new supercomputer architectures are discussed.

Details

Engineering Computations, vol. 4 no. 3
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 17 October 2008

Lei Yang, James Dankert and Jennie Si

The purpose of this paper is to develop a mathematical framework to address some algorithmic features of approximate dynamic programming (ADP) by using an average cost formulation…

Abstract

Purpose

The purpose of this paper is to develop a mathematical framework to address some algorithmic features of approximate dynamic programming (ADP) by using an average cost formulation based on the concepts of differential costs and performance gradients. Under such a framework, a modified value iteration algorithm is developed that is easy to implement, in the mean time it can address a class of partially observable Markov decision processes (POMDP).

Design/methodology/approach

Gradient‐based policy iteration (GBPI) is a top‐down, system‐theoretic approach to dynamic optimization with performance guarantees. In this paper, a bottom‐up, algorithmic view is provided to complement the original high‐level development of GBPI. A modified value iteration is introduced, which can provide solutions to the same type of POMDP problems dealt with by GBPI. Numerical simulations are conducted to include a queuing problem and a maze problem to illustrate and verify features of the proposed algorithms as compared to GBPI.

Findings

The direct connection between GBPI and policy iteration is shown under a Markov decision process formulation. As such, additional analytical insights were gained on GBPI. Furthermore, motivated by this analytical framework, the authors propose a modified value iteration as an alternative to addressing the same POMDP problem handled by GBPI.

Originality/value

Several important insights are gained from the analytical framework, which motivate the development of both algorithms. Built on this paradigm, new ADP learning algorithms can be developed, in this case, the modified value iteration, to address a broader class of problems, the POMDP. In addition, it is now possible to provide ADP algorithms with a gradient perspective. Inspired by the fundamental understanding of learning and optimization problems under the gradient‐based framework, additional new insight may be developed for bottom‐up type of algorithms with performance guarantees.

Details

International Journal of Intelligent Computing and Cybernetics, vol. 1 no. 4
Type: Research Article
ISSN: 1756-378X

Keywords

Article
Publication date: 20 July 2010

Zvi Goldstein, David Petrie and Yosef Sherif

The purpose of this paper is to advance a dynamic programming model that encompasses critical attributes of plan‐driven development, rapid development, agile development, and the…

1248

Abstract

Purpose

The purpose of this paper is to advance a dynamic programming model that encompasses critical attributes of plan‐driven development, rapid development, agile development, and the hybrid open source development. The paper aims to put forward a middle ground management strategy for software development to gain more effectiveness and efficiency in delivering projects on time and within budget.

Design/methodology/approach

The paper combines narrative with argument and analysis with a dynamic programming model. The model was applied to numerical cases with different project operating costs, duration, expected setup costs for a development iteration, and business penalties for a failed iteration. Sensitivity analysis is performed by changing several parameters and observing the effects these changes have on the optimal solution.

Findings

The model delivers a middle ground management strategy for software development and obtains an optimal solution that is better than if a project used one specific development methodology.

Originality/value

The paper demonstrates how the dynamic programming model when used with middle ground management strategy would produce the ultimate goal of delivering projects on time and within budget.

Details

Information Management & Computer Security, vol. 18 no. 3
Type: Research Article
ISSN: 0968-5227

Keywords

Open Access
Article
Publication date: 5 March 2021

Julee Srivastava

In this paper, Picard–S hybrid iterative process is defined, which is a hybrid of Picard and S-iterative process. This new iteration converges faster than all of Picard…

Abstract

Purpose

In this paper, Picard–S hybrid iterative process is defined, which is a hybrid of Picard and S-iterative process. This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid and Picard–Ishikawa hybrid iterative processes for contraction mappings and to find the solution of delay differential equation, using this hybrid iteration also proved some results for Picard–S hybrid iterative process for nonexpansive mappings.

Design/methodology/approach

This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative processes for contraction mappings.

Findings

Showed the fastest convergence of this new iteration and then other iteration defined in this paper. The author finds the solution of delay differential equation using this hybrid iteration. For new iteration, the author also proved a theorem for nonexpansive mapping.

Originality/value

This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative processes for contraction mappings and to find the solution of delay differential equation, using this hybrid iteration also proved some results for Picard–S hybrid iterative process for nonexpansive mappings.

Details

Arab Journal of Mathematical Sciences, vol. 28 no. 1
Type: Research Article
ISSN: 1319-5166

Keywords

Article
Publication date: 1 February 1982

I. MAYERGOYZ

New iteration methods for the calculation of steady magnetic fields in saturable media are presented. These methods converge for any choice of initial approximation, that is they…

Abstract

New iteration methods for the calculation of steady magnetic fields in saturable media are presented. These methods converge for any choice of initial approximation, that is they possess global convergence. The convergence conditions and the estimates of convergence rate of these methods are expressed in terms of the physical properties of ferromagnetic media. Each of the proposed methods is deliberately adapted to specific but typical saturation conditions. All these methods together cover the broad area of diverse saturation conditions encountered in practice. The construction and justification of these iteration methods are based on the physical concept of secondary sources and on some mathematical ideas and results arising in the overlapping area of mathematical physics and functional analysis.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 1 no. 2
Type: Research Article
ISSN: 0332-1649

Article
Publication date: 1 February 2006

Ian M. Smith and Lee Margetts

To investigate the cause of a well‐known phenomenon associated with a range of parallel iterative solvers – the variability in the number of iterations required to achieve…

Abstract

Purpose

To investigate the cause of a well‐known phenomenon associated with a range of parallel iterative solvers – the variability in the number of iterations required to achieve convergence.

Design/methodology/approach

The conclusions are based on extensive experiments undertaken using parallel computers. Recently published works are also used to provide additional examples of variability in iteration count.

Findings

The variability of iteration counts experienced by parallelised, element‐by‐element iterative solvers is caused by numerical precision and roundoff.

Research limitations/implications

A theoretical examination of the phenomenon may bring to light a methodology in which the iteration count could be limited to the lower end of the variable range – thus reducing solution times.

Practical implications

The authors believe that the variability in iteration count described for element‐by‐element methods presents no real difficulty to the engineering analyst.

Originality/value

The paper gives a detailed account of the phenomenon and is useful both to developers of parallel iterative solvers and to the analysts that use them in practice.

Details

Engineering Computations, vol. 23 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 3 May 2019

Jin-Ping Wang, Jian-Fei Zhang, Zhi-Guo Qu and Wen-Quan Tao

Pressure-based methods have been demonstrated to be powerful for solving many practical problems in engineering. In many pressure-based methods, inner iterative processes are…

134

Abstract

Purpose

Pressure-based methods have been demonstrated to be powerful for solving many practical problems in engineering. In many pressure-based methods, inner iterative processes are proposed to get efficient solutions. However, the number of inner iterations is set empirically and kept fixed during the whole computation for different problems, which is overestimated in some computations but underestimated in other computations. This paper aims to develop an algorithm with adaptive inner iteration processes for steady and unsteady incompressible flows.

Design/methodology/approach

In this work, with the use of two different criteria in two inner iterative processes, a mechanism is proposed to control inner iteration processes to make the number of inner iterations vary during computing according to different problems. By doing so, adaptive inner iteration processes can be achieved.

Findings

The adaptive inner iterative algorithm is verified to be valid by solving classic steady and unsteady incompressible problems. Results show that the adaptive inner iteration algorithm works more efficient than the fixed inner iteration one.

Originality/value

The algorithm with adaptive inner iteration processes is first proposed in this paper. As the mechanism for controlling inner iteration processes is based on physical meaning and the feature of iterative calculations, it can be used in any methods where there exist inner iteration processes. It is not limited for incompressible flows. The performance of the adaptive inner iteration processes in compressible flows is conducted in a further study.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 5 June 2009

Danilo Ferreira de Carvalho and Carmelo José Albanez Bastos‐Filho

Particle swarm optimization (PSO) has been used to solve many different types of optimization problems. In spite of this, the original version of PSO is not capable to find…

Abstract

Purpose

Particle swarm optimization (PSO) has been used to solve many different types of optimization problems. In spite of this, the original version of PSO is not capable to find reasonable solutions for some types of problems. Therefore, novel approaches to deal with more sophisticated problems are required. Many variations of the basic PSO form have been explored, targeting the velocity update equation. Other approaches attempt to change the communication topology inside the swarm. The purpose of this paper is to propose a topology based on the concept of clans.

Design/methodology/approach

First of all, this paper presents a detailed description of its proposal. After that, it shows a graphical convergence analysis for the Rosenbrock benchmark function. In the sequence, a convergence analysis for clan PSO with different parameters is performed. A comparison with star, ring, focal, von Neumann and four clusters topologies is also performed.

Findings

The paper's simulation results have shown that the proposal obtained better results than the other topologies for the benchmark functions selected for this paper.

Originality/value

The proposed topology for PSO based on clans provides a novel form for information distribution inside the swarm. In this approach, the topology is determined dynamically during the search process, according to the success rate inside each clan.

Details

International Journal of Intelligent Computing and Cybernetics, vol. 2 no. 2
Type: Research Article
ISSN: 1756-378X

Keywords

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