14 research outputs found

    MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

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    Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

    Generalized averaged Gaussian quadrature and applications

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    A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

    Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

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    This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions

    5th EUROMECH nonlinear dynamics conference, August 7-12, 2005 Eindhoven : book of abstracts

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    5th EUROMECH nonlinear dynamics conference, August 7-12, 2005 Eindhoven : book of abstracts

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    Molecular Dynamics Simulation

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    Condensed matter systems, ranging from simple fluids and solids to complex multicomponent materials and even biological matter, are governed by well understood laws of physics, within the formal theoretical framework of quantum theory and statistical mechanics. On the relevant scales of length and time, the appropriate ‘first-principles’ description needs only the Schroedinger equation together with Gibbs averaging over the relevant statistical ensemble. However, this program cannot be carried out straightforwardly—dealing with electron correlations is still a challenge for the methods of quantum chemistry. Similarly, standard statistical mechanics makes precise explicit statements only on the properties of systems for which the many-body problem can be effectively reduced to one of independent particles or quasi-particles. [...

    Lineer olmayan sobolev türü kısmi türevli diferansiyel denklemlerin tanh-coth yöntemi ile çözümü

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    06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.Birçok fiziksel olguyu açıklayan Sobolev türü denklemler, boyuta ve zamana bağlı türevleri, en yüksek mertebeden türevli terimlerinde bulundurmaları ile karakterize edilmektedir. En yüksek mertebeli türevlerinde sadece bir tane zamana bağlı türev bulunduran denklemler ise pseudoparabolik denklem olarak adlandırılır ve bu denklemler Sobolev türü denklemlerin özel bir durumudur. Bu çalıĢmada iyi bilinen Sobolev ve pseudoparabolik denklem türleri ele alınmıĢ ve bu denklemlerin genel özellikleri verilmiĢtir. Tanh-coth yöntemi lineer olmayan kısmi türevli diferansiyel denklemlerin hareketli dalga çözümlerini bulmada etkili ve güvenilir bir yöntemdir. Bugüne kadar bu yöntem yoğun olarak kullanılmıĢ ve yöntemin Riccati denklemi kullanılarak elde edilen modifikasyonları literatürde tartıĢılmıĢtır. Bu tezde, tanh-coth yönteminin temel özellikleri ve bu yöntemin diğer uzantıları ele alınmıĢtır. Buna ek olarak tanhcoth yöntemi, sembolik hesaplama sistemleri yardımıyla Sobolev türü denklemlerin tam çözümlerini araĢtırmada kullanılmıĢ ve bu denklemlerin birçok hareketli dalga çözümü elde edilmiĢtir. Elde edilen bu sonuçlar daha önce elde edilen bilgilerin bir doğrulaması ve geliĢtirilmesi olarak görülebilir. ÇalıĢma boyunca, cebirsel iĢlemler için Maple ve Scientific Work Place programları kullanılmıĢtır.Sobolev type equations have been used to describe many physical phenomena and they are characterized by having mixed time and space derivatives appearing in the highest-order terms of an partial differential equation. Equations with a one time derivative appearing in the highest order term are called pseudoparabolic and they are special case of Sobolev equations. In this work, well-known Sobolev and pseudoparabolic type equations have been considered and general properties of these equations have been given. The tanh-coth is a powerful and reliable technique for finding travelling wave solutions for nonlinear partial differential equations. This method has been used extensively and it was subjected by some modifications using the Riccati equation. The main features of the tanh-coth method and various extension forms of this method have been discussed in this thesis. Furthermore, the tanh-coth method with the aid of symbolic computational systems has been employed to investigate exact solutions of Sobolev type equations and abundant travelling wave solutions have been found. The results obtained can be viewed as a verification and improvement of the previously known data. Throughout the study, Maple and Scientific Work Place was used to deal with the tedious algebraic operations
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