Search results for: global convergence

Authors: Guettal Djaouida, Ziadi Abdelkader

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In this paper, we study a coupling of the Alienor method with the algorithm of Piyavskii-Shubert. The classical multidimensional global optimization methods involves great difficulties for their implementation to high dimensions. The Alienor method allows to transform a multivariable function into a function of a single variable for which it is possible to use efficient and rapid method for calculating the the global optimum. This simplification is based on the using of a reducing transformation called Alienor.

Keywords: global optimization, reducing transformation, α-dense curves, Alienor method, Piyavskii-Shubert algorithm

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Authors: Ramin Javadzadeh

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The particle swarm optimization are Meta heuristic optimization method, which are used for clustering and pattern recognition applications are abundantly. These algorithms in multimodal optimization problems are more efficient than genetic algorithms. A major drawback in these algorithms is their slow convergence to global optimum and their weak stability can be considered in various running of these algorithms. In this paper, improved Particle swarm optimization is introduced for the first time to overcome its problems. The fuzzy cellular automata is used for improving the algorithm efficiently. The credibility of the proposed approach is evaluated by simulations, and it is shown that the proposed approach achieves better results can be achieved compared to the Particle swarm optimization algorithms.

Keywords: cellular automata, cellular learning automata, local search, optimization, particle swarm optimization

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Authors: Y. A. Yahaya, Ahmad Tijjani Asabe

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This paper focuses on the formulation of 3-step hybrid Adams type method for the solution of first order differential equation (ODE). The methods which was derived on both grid and off grid points using multistep collocation schemes and also evaluated at some points to produced Block Adams type method and Adams moulton method respectively. The method with the highest order was selected to serve as the corrector. The convergence was valid and efficient. The numerical experiments were carried out and reveal that hybrid Adams type methods performed better than the conventional Adams moulton method.

Keywords: adam-moulton type (amt), corrector method, off-grid, block method, convergence analysis

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Authors: Hram Bik

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This is an analytical paper on how to apply theology to the global godless culture. The paper will analyze and materialize theology of culture and come up with theo-cultural principles which will enable Christians to properly engage with today godless culture. If theology and daily life are in any way split apart, Christians will lose the authenticity essential to their calling. Living out godliness in the ungodly culture requires materializing theology into daily life. To do that has become an unbeatable challenge for Christians in 21st century with the overtaking in of global godless culture enforced by Information Technology resulting in rapid and chaotic change of global lifestyles wherein Christianity stands in danger of being swallowed up. Staying away from the culture will rob Christianity of its mission to witness and staying with and like it will rob Christianity of its effectiveness. Thus the question is how should today Christians apply theology to the culture wherein what are said to be sins in the Bible no longer look like sins? Should we forge an all-out war against it or should distance ourselves away from it? The extreme response to it could fruit Christian Jihadism on the right and the apathetic response would let it booming with no one attempting to stop it on the left. This paper calls for global Christians to essentially make theology a part of their daily lives to form a united global force to influence the godless global culture by influencing our own family and community.

Keywords: Christians, global culture, godliness, theology

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Authors: Igor Velickovski, Aleksandar Stojkov, Ivana Rajkovic

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This paper investigates drivers of shock synchronization using quarterly data for 27 European countries over the period 1999-2013 and taking into account the difference between core (‘the euro area core locomotive’) and peripheral euro area and transition countries (‘the peripheral wagons’). Results from panel error-correction models suggest that core of the euro area has not been strong magnetizer of the shock convergence of periphery and transition countries since the euro inception as a result of the offsetting effects of the various factors that affected the shock convergence process. These findings challenge the endogeneity hypothesis in the optimum currency area framework and rather support the specialisation paradigm which is concerning evidence for the future stability of the euro area.

Keywords: dynamic panel models, shock synchronisation, trade, optimum currency area

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Authors: Malika Fekih, Abdenour Bourabaa, Rafika Hariti, Mohamed Saighi

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In Algeria the global solar radiation and its components is not available for all locations due to which there is a requirement of using different models for the estimation of global solar radiation that use climatological parameters of the locations. Empirical constants for these models have been estimated and the results obtained have been tested statistically. The results show encouraging agreement between estimated and measured values.

Keywords: global solar radiation, empirical model, semi arid areas, climatological parameters

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Authors: Sandeep Singh

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In this article, two classes of iterative schemes are proposed for approximating solutions of nonlinear systems of equations whose orders of convergence are six and eight respectively. Sixth order scheme requires the evaluation of two vector-functions, two first Fr'echet derivatives and three matrices inversion per iteration. This three-step sixth-order method is further extended to eighth-order method which requires one more step and the evaluation of one extra vector-function. Moreover, computational efficiency is compared with some other recently published methods in which we found, our methods are more efficient than existing numerical methods for higher and medium size nonlinear system of equations. Numerical tests are performed to validate the proposed schemes.

Keywords: Nonlinear systems, Computational complexity, order of convergence, Jarratt-type scheme

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Authors: R. Sabre

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This work focuses on the symmetric alpha stable process with continuous time frequently used in modeling the signal with indefinitely growing variance, often observed with an unknown additive error. The objective of this paper is to estimate this error from discrete observations of the signal. For that, we propose a method based on the smoothing of the observations via Jackson polynomial kernel and taking into account the width of the interval where the spectral density is non-zero. This technique allows avoiding the “Aliasing phenomenon” encountered when the estimation is made from the discrete observations of a process with continuous time. We have studied the convergence rate of the estimator and have shown that the convergence rate improves in the case where the spectral density is zero at the origin. Thus, we set up an estimator of the additive error that can be subtracted for approaching the original signal without error.

Keywords: spectral density, stable processes, aliasing, non parametric

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Authors: Asma Moomal, Zukarnain Zakaria

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In this uncertain, highly competitive and hasty moving era, most of the organizations are surviving under the pressure of complex dynamics, fierce competition and many challenges in terms of global talent management within the global market. One key result of these challenges is that the organizations have to be organized and good at handling human capital if they want to gain sustainable and steady success in near future. By keeping in mind the importance of global competition, many human resource (HR) professionals are diagnosing the complexities in managing talent of human capital at global level, especially those of multinational enterprises (MNEs). As, there has been little research in the country regarding identification of the GTM in MNEs, this paper reviewed the relevant literature in order to examine the role of GTM strategies in enhancing the organizational development in the MNEs of Malaysia. The data collection technique used in this study was done through the secondary data resources (i.e. the existing literature analysis). This study contributes to extend our understanding of the impact of GTM on organizational development of MNEs within the country.

Keywords: Global Talent Management (GTM), multinational enterprises (MNEs), organizational development, talent

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Authors: Arzu K. Kamberli

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This article examines the relationship between economics and physics, starting with Adam Smith, with a new econophysics approach in Economics-Physics with the Gauss Law model proposal using for the Electric Field calculation, which will allow us to anticipate the Global Financial Crisis. For this purpose, the similarities between the Gauss Law using the electric field calculations and the global financial crisis have been explained on the formula, and a model has been suggested to predict the risks of the financial systems from the electricity field calculations. Thus, this study is expected to help for preventing the Global Financial Crisis with the contribution of the science of economics and physics from the aspect of econophysics.

Keywords: econophysics, electric field, financial system, Gauss law, global financial crisis

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Authors: Andreas Aceranti, Stefano Costa

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The aim of this study was to demonstrate that manipulative treatment combined with therapeutic exercisetherapywas more effective than isolated therapeutic exercise in the short-term treatment of eye convergence disorders in boxers. A randomized controlled trial (RCT) pilot trial was performed at our physiotherapy practices. 30 adult subjects who practice the discipline of boxing were selected after an initial skimming defined by the Convergence Insufficiency Symptom Survey (CISS) test (results greater than or equal to 10) starting from the initial sample of 50 subjects; The 30 recruits were evaluated by an orthoptist using prisms to know the diopters of each eye and were divided into 2 groups (experimental group and control group). The members of the experimental group were subjected to manipulation of the lateral strain of sphenoid from the side contralateral to the eye that had fewer diopters and were subjected to a sequence of 3 ocular motor exercises immediately after manipulation. The control group, on the other hand, received only ocular motor treatment. A secondary outcome was also drawn up that demonstrated how changes in ocular motricity also affected cervical rotation. Analysis of the data showed that the experimental treatment was in the short term superior to the control group to astatistically significant extent both in terms of the prismatic delta of the right eye (0 OT median without manipulation and 10 OT median with manipulation) and that of the left eye (0 OT median without manipulation and 5 OT median with manipulation). Cervical rotation values also showed better values in the experimental group with a median of 4° in the right rotation without manipulation and 6° with thrust; the left rotation presented a median of 2° without manipulation and 7° with thrust. From the results that emerged, the treatment was effective. It would be desirable to increase the sample number and set up a timeline to see if the net improvements obtained in the short term will also be maintained in the medium to long term.

Keywords: boxing, basilar spheno synchondrosis, ocular convergence deficit, osteopathic treatment

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Authors: Analen Malnegro, Gina Malacas

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Dominating sets and related topics have been studied extensively in the past few decades. A dominating set of a graph G is a subset D of V such that every vertex not in D is adjacent to at least one member of D. The domination number γ(G) is the number of vertices in a smallest dominating set for G. Some problems involving detection devices can be modeled with graphs. Finding the minimum number of devices needed according to the type of devices and the necessity of locating the object gives rise to locating-dominating sets. A subset S of vertices of a graph G is called locating-dominating set, LD-set for short, if it is a dominating set and if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. The location-domination number λ(G) is the minimum cardinality of an LD-set for G. The complement of a graph G is a graph Ḡ on same vertices such that two distinct vertices of Ḡ are adjacent if and only if they are not adjacent in G. An LD-set of a graph G is global if it is an LD-set of both G and its complement Ḡ. The global location-domination number λg(G) is defined as the minimum cardinality of a global LD-set of G. In this paper, global LD-sets on the join of two graphs are characterized. Global location-domination numbers of these graphs are also determined.

Keywords: dominating set, global locating-dominating set, global location-domination number, locating-dominating set, location-domination number

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Authors: Seyed Sajjad Habibi

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The aim of this study is to investigate the impact of global financial crises and corporate financial crisis on tax evasion of companies listed on the Tehran Stock Exchange. For this purpose, panel data in the periods of financial crisis period (2007 to 2012) and without a financial crisis (2004, 2005, 2006, 2013, 2014, and 2015) was analyzed using multivariate linear regression. The results indicate a significant relationship between the corporate financial crisis (bankruptcy risk) and tax evasion in the global financial crisis period. The results also showed a significant relationship between the corporate bankruptcy risk and tax evasion in the period with no global financial crisis. A significant difference was found between the bankruptcy risk and tax evasion in the period of the global financial crisis and that with no financial crisis so that tax evasion increased in the financial crisis period.

Keywords: global financial crisis, corporate financial crisis, bankruptcy risk, tax evasion risk, emerging markets

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Authors: Ali Al-Zughaibi

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The purpose of this paper is to present a modeling and control of the quarter car active suspension system with unknown mass, unknown time-delay and road disturbance. The objective of designing the controller by deriving a control law to achieve stability of the system and convergence that can considerably improve the ride comfort and road disturbance handling. Thus is accomplished by using Routh-Herwitz criterion and based on some assumptions. A mathematical proof is given to show the ability of the designed controller to ensure stability and convergence of the active suspension system and dispersion oscillation of system with unknown mass, time-delay and road disturbances. Simulations were also performed for controlling quarter car suspension, where the results obtained from these simulations verify the validity of the proposed design.

Keywords: active suspension system, time-delay, disturbance rejection, dynamic uncertainty

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Authors: Sachin Aggarwal, Sarah Kassinger, Nicholas Hoffman

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Geometry simplification is a key step in performing conjugate heat transfer analysis using CFD. This paper proposes a standard methodology for the geometry simplification of rotating machines, such as electrical generators and electrical motors (both air and liquid-cooled). These machines are extensively deployed throughout the aerospace and automotive industries, where optimization of weight, volume, and performance is paramount -especially given the current global transition to renewable energy sources and vehicle hybridization and electrification. Conjugate heat transfer analysis is an essential step in optimizing their complex design. This methodology will help in reducing convergence issues due to poor mesh quality, thus decreasing computational cost and overall analysis time.

Keywords: CFD, electrical machines, Geometry simplification, heat transfer

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Authors: Chad Brown

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This paper establishes general conditions for the convergence rates of nonparametric sieve estimators with dependent data. We present two key results: one for nonstationary data and another for stationary mixing data. Previous theoretical results often lack practical applicability to deep neural networks (DNNs). Using these conditions, we derive convergence rates for DNN sieve estimators in nonparametric regression settings with both nonstationary and stationary mixing data. The DNN architectures considered adhere to current industry standards, featuring fully connected feedforward networks with rectified linear unit activation functions, unbounded weights, and a width and depth that grows with sample size.

Keywords: sieve extremum estimates, nonparametric estimation, deep learning, neural networks, rectified linear unit, nonstationary processes

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Authors: Alexander Hempfing

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The desire to understand business cycle fluctuations, trade interdependencies and co-movement has a long tradition in economic thinking. From input-output economics to business cycle theory, researchers aimed to find appropriate answers from an empirical as well as a theoretical perspective. This paper empirically analyses how the production structure of the global economy and several states developed over time, what their distributional properties are and if there are network specific metrics that allow identifying structurally important nodes, on a global, national and sectoral scale. For this, the World Input-Output Database was used, and different statistical methods were applied. Empirical evidence is provided that the importance of the Eastern hemisphere in the global production network has increased significantly between 2000 and 2014. Moreover, it was possible to show that the sectoral eigenvector centrality indices on a global level are power-law distributed, providing evidence that specific national sectors exist which are more critical to the world economy than others while serving as a hub within the global production network. However, further findings suggest, that global production cannot be characterized as a scale-free network.

Keywords: economic integration, industrial organization, input-output economics, network economics, production networks

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Authors: Safeer Hussain Khan, H. Fukhar-ud-Din

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The concept of quasi-contractive type operators was given by Berinde and extended by Imoru and Olatinwo. They named this new type as contractive-like operators. On the other hand, Xu and Noo introduced a three-step-one-mappings iterative process which can be seen as a generalization of Mann and Ishikawa iterative processes. Approximating common fixed points has its own importance as it has a direct link with minimization problem. Motivated by this, in this paper, we first extend the iterative process of Xu and Noor to the case of three-step-three-mappings and then prove a strong convergence result using contractive-like operators for this iterative process. In general, this generalizes corresponding results using Mann, Ishikawa and Xu-Noor iterative processes with quasi-contractive type operators. It is to be pointed out that our results can also be proved with iterative process involving error terms.

Keywords: contractive-like operator, iterative process, common fixed point, strong convergence

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Authors: Erick Pruchnicki, Nikhil Padhye

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Plates are important engineering structures which have attracted extensive research since the 19th century. The subject of this work is statical analysis of a linearly elastic homogenous plate under small deformations. A 'thin plate' is a three-dimensional structure comprising of a small transverse dimension with respect to a flat mid-surface. The general aim of any plate theory is to deduce a two-dimensional model, in terms of mid-surface quantities, to approximately and accurately describe the plate's deformation in terms of mid-surface quantities. In recent decades, a common starting point for this purpose is to utilize series expansion of a displacement field across the thickness dimension in terms of the thickness parameter (h). These attempts are mathematically consistent in deriving leading-order plate theories based on certain a priori scaling between the thickness and the applied loads; for example, asymptotic methods which are aimed at generating leading-order two-dimensional variational problems by postulating formal asymptotic expansion of the displacement fields. Such methods rigorously generate a hierarchy of two-dimensional models depending on the order of magnitude of the applied load with respect to the plate-thickness. However, in practice, applied loads are external and thus not directly linked or dependent on the geometry/thickness of the plate; thus, rendering any such model (based on a priori scaling) of limited practical utility. In other words, the main limitation of these approaches is that they do not furnish a single plate model for all orders of applied loads. Following analogy of recent efforts of deploying Fourier-series expansion to study convergence of reduced models, we propose two-dimensional model(s) resulting from truncation of the potential energy and rigorously prove the convergence of these two-dimensional plate models to the parent three-dimensional linear elasticity with increasing truncation order of the potential energy.

Keywords: plate theory, Fourier-series expansion, convergence result, Legendre polynomials

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Authors: Amna Batool

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Agile methodology is the current most popular technique in software development projects. Agile methods in software development bring optimistic impact on software performances, quality and customer satisfaction. There are some organizations and small-medium enterprises adopting agile into their local software development projects as well as in distributed software development projects. Adopting agile methods in local software development projects is valuable. However, agile global software deployment needs an attention. There are different key challenges in agile global software development that need to resolve and enhance the global software development cycles. The proposed systematic literature review investigates all key challenges of agile in global software development. Moreover, a quantitative methodology (an actual survey) targeted to present a real case scenario of these particular key challenges faced by one of the software houses that is BestWeb Malaysia. The outcomes of systematic literature and the results of quantitative methodology are compared with each other to evaluate if the key challenges pointed out in systematic review still exist. The proposed research and its exploratory results can assist small medium enterprises to avoid these challenges by adopting the best practices in their global software development projects. Moreover, it is helpful for novice researchers to get valuable information altogether.

Keywords: agile software development, ASD challenges, agile global software development, challenges in agile global software development

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Authors: S. H. Arnaud Kanga, O. Hili, S. Dabo-Niang

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Spatial prediction is an issue appealing and attracting several fields such as agriculture, environmental sciences, ecology, econometrics, and many others. Although multiple non-parametric prediction methods exist for spatial data, those are based on the conditional expectation. This paper took a different approach by examining a non-parametric spatial predictor of the conditional quantile. The study especially observes the stationary multidimensional spatial process over a rectangular domain. Indeed, the proposed quantile is obtained by inverting the conditional distribution function. Furthermore, the proposed estimator of the conditional distribution function depends on three kernels, where one of them controls the distance between spatial locations, while the other two control the distance between observations. In addition, the almost complete convergence and the convergence in mean order q of the kernel predictor are obtained when the sample considered is alpha-mixing. Such approach of the prediction method gives the advantage of accuracy as it overcomes sensitivity to extreme and outliers values.

Keywords: conditional quantile, kernel, nonparametric, stationary

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Authors: Ali Atashbar Orang, Carlo Massimo Casciola

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A novel numerical approach for the steady incompressible turbulent flows is presented in this paper. The artificial compressibility method (ACM) is applied to the Reynolds Averaged Navier-Stokes (RANS) equations. A new Characteristic-Based Turbulent (CBT) scheme is developed for the convective fluxes. The well-known Spalart–Allmaras turbulence model is employed to check the effectiveness of this new scheme. Comparing the proposed scheme with previous studies, it is found that the present CBT scheme demonstrates accurate results, high stability and faster convergence. In addition, the local time stepping and implicit residual smoothing are applied as the convergence acceleration techniques. The turbulent flows past a backward facing step, circular cylinder, and NACA0012 hydrofoil are studied as benchmarks. Results compare favorably with those of other available schemes.

Keywords: incompressible turbulent flow, method of characteristics, finite volume, Spalart–Allmaras turbulence model

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Authors: Ahmed R. Abdelaziz, Zaki M. I. Osha

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Solar radiation data are of great significance for solar energy system design. This study aims at developing and calibrating new empirical models for estimating monthly mean daily global solar radiation on a horizontal surface in Alexandria, Egypt. Day length hours, sun height, day number, and declination angle calculated data are used for this purpose. A comparison between measured and calculated values of solar radiation is carried out. It is shown that all the proposed correlations are able to predict the global solar radiation with excellent accuracy in Alexandria.

Keywords: solar energy, global solar radiation, model, regression coefficient

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Authors: Indu Gupta

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Climate change and global warming is most burning issue for “our common future”. For this common global interest. Countries organize conferences of government and nongovernment type. Human being destroying the non-renewable resources and polluting the renewable resources of planet for economic growth. Air pollution is mainly responsible for global warming and climate change .Due to global warming ice glaciers are shrinking and melting. Forests are shrinking, deserts expanding and soil eroding. The depletion of stratospheric ozone layer is depleting and hole in ozone layer that protect us from harmful ultra violet radiation. Extreme high temperature in summer and extreme low temperature and smog in winters, floods in rainy season. These all are indication of climate change. The level of carbon dioxide and other heat trapping gases in the atmosphere is increasing at high speed. Nation’s are worried about environmental degradation.

Keywords: environmental degradation, global warming, soil eroding, ultra-Violate radiation

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Authors: Dagaci Aliyu Manbe, Anthony Abah Ebonyi

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The increase in global temperatures is worsened by frequent natural events and human activities. Climate change has taken a prominent space in the global discourse on crime and criminality. Compared to when the subject centred around the discussion on the depletion of the ozone layer and global warming, today, the narrative revolves around the implications of changes in weather and climatic conditions in relations to violent crimes or conflict that traverse vast social, economic, and political spaces in different countries. Global warming and climate change refer to an increase in average global temperatures in the Earth’s near-surface air and oceans, which occurs due to human activities such as deforestation and the burning of fossil fuel such as gas flaring. The trend is projected to continue, if unchecked. This paper seeks to explore the nexus between climate change and criminality in Nigeria. It further examines the main ecological changes that predispose conflict dynamics of security threats factored by climate change to peaceful co-existence in Nigeria. It concludes with some recommendations on the way forward.

Keywords: conflict, climate change, criminality, global warning, peace

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Authors: In Hoi Lee, Seong Baeg Kim, Je Eung Jeon, Gwang Yong Choi, Joo Sub Lee, Ik Sang Kim

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Recently, the interest of globalization in the field of teacher education has increased. In the U.S., the government is trying to enhance the quality of education through a global approach in education. To do so, the schools in the U.S. are recruiting teachers with global capability from countries like Korea where competent teachers are being trained. Meanwhile, in the case of Korea, although excellent teachers have been cultivated every year, due to a low birth rate it is not easy to become a domestic teacher. To solve the trouble that the two countries are facing, the study first examines the demand and necessity of globalization in the field of teacher education between Korea and the U.S. Second, we propose a new project, called the ‘Global Teachers University (GTU)’ program to satisfy the demands of both countries. Finally, we provide its implications to build the future educational cooperation for teacher training in a global context.

Keywords: educational cooperation, globalization, teachers education program, teacher training institutions

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Authors: Belloufi Mohammed, Sellami Badreddine

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This paper deals with a new nonlinear modified three-term conjugate gradient algorithm for solving large-scale unstrained optimization problems. The search direction of the algorithms from this class has three terms and is computed as modifications of the classical conjugate gradient algorithms to satisfy both the descent and the conjugacy conditions. An example of three-term conjugate gradient algorithm from this class, as modifications of the classical and well known Hestenes and Stiefel or of the CG_DESCENT by Hager and Zhang conjugate gradient algorithms, satisfying both the descent and the conjugacy conditions is presented. Under mild conditions, we prove that the modified three-term conjugate gradient algorithm with Wolfe type line search is globally convergent. Preliminary numerical results show the proposed method is very promising.

Keywords: unconstrained optimization, three-term conjugate gradient, sufficient descent property, line search

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Authors: Fariborz Ahmadi, Reza Tati

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Genetic algorithm is a soft computing method that works on set of solutions. These solutions are called chromosome and the best one is the absolute solution of the problem. The main problem of this algorithm is that after passing through some generations, it may be produced some chromosomes that had been produced in some generations ago that causes reducing the convergence speed. From another respective, most of the genetic algorithms are implemented in software and less works have been done on hardware implementation. Our work implements genetic algorithm in hardware that doesn’t produce chromosome that have been produced in previous generations. In this work, most of genetic operators are implemented without producing iterative chromosomes and genetic diversity is preserved. Genetic diversity causes that not only do not this algorithm converge to local optimum but also reaching to global optimum. Without any doubts, proposed approach is so faster than software implementations. Evaluation results also show the proposed approach is faster than hardware ones.

Keywords: hardware, genetic algorithm, computer science, engineering

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Authors: Zafer Cakmak, Birol Bulut, Cengiz Taskiran

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Technological advances, the world becoming smaller and increasing world population increase our interdependence with individuals that we maybe never meet face to face. It is impossible for the modern individuals to escape global developments and their impact. Furthermore, it is very unlikely for the global societies to turn back from the path they are in. These effects of globalization in fact encumber the humankind at a certain extend. We succumb to these responsibilities for we desire a better future, a habitable world and a more peaceful life. In the present study, global responsibility levels of the participants were measured and the significance of global reactions that individuals have to develop on global issues was reinterpreted under the light of the existing literature. The study was conducted with general survey model, one of the survey methodologies General survey models are surveys conducted on the whole universe or a group, sample or sampling taken from the universe to arrive at a conclusion about the universe, which includes a high number of elements. The study was conducted with data obtained from 350 pre-service teachers attending 2016 spring semester to determine 'Global Social Responsibility' levels of social studies pre-service teachers based on several variables. Collected data were analyzed using SPSS 21.0 software. T-test and ANOVA were utilized in the data analysis.

Keywords: social studies, globalization, global social responsibility, education

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Authors: Harendra Singh, Rajesh Pandey

Abstract:

The paper presents a numerical method based on operational matrix of integration and Ryleigh method for the solution of a class of non-linear fractional variational problems (NLFVPs). Chebyshev first kind polynomials are used for the construction of operational matrix. Using operational matrix and Ryleigh method the NLFVP is converted into a system of non-linear algebraic equations, and solving these equations we obtained approximate solution for NLFVPs. Convergence analysis of the proposed method is provided. Numerical experiment is done to show the applicability of the proposed numerical method. The obtained numerical results are compared with exact solution and solution obtained from Chebyshev third kind. Further the results are shown graphically for different fractional order involved in the problems.

Keywords: non-linear fractional variational problems, Rayleigh-Ritz method, convergence analysis, error analysis

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