Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations PDF Download

Author: Santanu Saha Ray
Publisher: CRC Press
ISBN: 1351682210
Category : Mathematics
Languages : en
Pages : 251

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Book Description
The main focus of the book is to implement wavelet based transform methods for solving problems of fractional order partial differential equations arising in modelling real physical phenomena. It explores analytical and numerical approximate solution obtained by wavelet methods for both classical and fractional order partial differential equations.

Author: Santanu Saha Ray
Publisher: CRC Press
ISBN: 1351682229
Category : Mathematics
Languages : en
Pages : 273

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Book Description
The main focus of the book is to implement wavelet based transform methods for solving problems of fractional order partial differential equations arising in modelling real physical phenomena. It explores analytical and numerical approximate solution obtained by wavelet methods for both classical and fractional order partial differential equations.

Author: Ülo Lepik
Publisher: Springer Science & Business Media
ISBN: 3319042955
Category : Technology & Engineering
Languages : en
Pages : 209

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Book Description
This is the first book to present a systematic review of applications of the Haar wavelet method for solving Calculus and Structural Mechanics problems. Haar wavelet-based solutions for a wide range of problems, such as various differential and integral equations, fractional equations, optimal control theory, buckling, bending and vibrations of elastic beams are considered. Numerical examples demonstrating the efficiency and accuracy of the Haar method are provided for all solutions.

Author: Reid
Publisher: Academic Press
ISBN: 0080955959
Category : Computers
Languages : en
Pages : 227

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Book Description
Riccati Differential Equations

Author: Christophe Tricaud
Publisher: Springer Science & Business Media
ISBN: 1447122623
Category : Technology & Engineering
Languages : en
Pages : 177

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Book Description
A successful cyber-physical system, a complex interweaving of hardware and software with some part of the physical environment, depends on proper identification of the, often pre-existing, physical element. A bespoke “cyber” part of the system may then be designed from scratch. Optimal Mobile Sensing and Actuation Strategies in Cyber-physical Systems focuses on distributed-parameter systems the dynamics of which can be modelled with partial differential equations. These are very challenging to observe, their states and inputs being distributed throughout a spatial domain. Consequently, systematic approaches to the optimization of sensor location have to be devised for parameter estimation. The text begins by reviewing the field of cyber-physical systems and introducing background notions of distributed parameter systems and optimal observation theory. New research problems are then defined within this framework. Two important problems considered are optimal mobile sensor trajectory planning and the accuracy effects and allocation of remote sensors. These are followed up with a solution to the problem of optimal robust estimation. Actuation policies are then introduced into the framework with the purpose of improving estimation and optimizing the trajectories of both sensors and actuators simultaneously. The large number of illustrations within the text will assist the reader to visualize the application of the methods proposed. A group of similar examples are used throughout the book to help the reader assimilate the material more easily. The monograph concentrates on the use of methods for which a cyber-physical-systems infrastructure is required. The methods are computationally heavy and require mobile sensors and actuators with communications abilities. Application examples cover fields from environmental science to national security so that readers are encouraged to link the ideas of cyber-physical systems with their own research.

Author: Santanu Saha Ray
Publisher: Springer Nature
ISBN: 9811516561
Category : Mathematics
Languages : en
Pages : 409

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Book Description
This book discusses various novel analytical and numerical methods for solving partial and fractional differential equations. Moreover, it presents selected numerical methods for solving stochastic point kinetic equations in nuclear reactor dynamics by using Euler–Maruyama and strong-order Taylor numerical methods. The book also shows how to arrive at new, exact solutions to various fractional differential equations, such as the time-fractional Burgers–Hopf equation, the (3+1)-dimensional time-fractional Khokhlov–Zabolotskaya–Kuznetsov equation, (3+1)-dimensional time-fractional KdV–Khokhlov–Zabolotskaya–Kuznetsov equation, fractional (2+1)-dimensional Davey–Stewartson equation, and integrable Davey–Stewartson-type equation. Many of the methods discussed are analytical–numerical, namely the modified decomposition method, a new two-step Adomian decomposition method, new approach to the Adomian decomposition method, modified homotopy analysis method with Fourier transform, modified fractional reduced differential transform method (MFRDTM), coupled fractional reduced differential transform method (CFRDTM), optimal homotopy asymptotic method, first integral method, and a solution procedure based on Haar wavelets and the operational matrices with function approximation. The book proposes for the first time a generalized order operational matrix of Haar wavelets, as well as new techniques (MFRDTM and CFRDTM) for solving fractional differential equations. Numerical methods used to solve stochastic point kinetic equations, like the Wiener process, Euler–Maruyama, and order 1.5 strong Taylor methods, are also discussed.

Author: Santanu Saha Ray
Publisher: Chapman & Hall/CRC
ISBN: 9780429771774
Category : Mathematics
Languages : en
Pages : 0

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Book Description
This book analyzes the various semi-analytical and analytical methods for finding approximate and exact solutions of fractional order partial differential equations. It explores approximate and exact solutions obtained by various analytical methods for fractional order partial differential equations arising in physical models.

Author: Boling Guo
Publisher: World Scientific
ISBN: 9814667064
Category : Mathematics
Languages : en
Pages : 347

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Book Description
This book aims to introduce some new trends and results on the study of the fractional differential equations, and to provide a good understanding of this field to beginners who are interested in this field, which is the authors' beautiful hope.This book describes theoretical and numerical aspects of the fractional partial differential equations, including the authors' researches in this field, such as the fractional Nonlinear Schrödinger equations, fractional Landau-Lifshitz equations and fractional Ginzburg-Landau equations. It also covers enough fundamental knowledge on the fractional derivatives and fractional integrals, and enough background of the fractional PDEs.

Author: Hemen Dutta
Publisher: John Wiley & Sons
ISBN: 1119654238
Category : Mathematics
Languages : en
Pages : 336

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Book Description
A guide to the new research in the field of fractional order analysis Fractional Order Analysis contains the most recent research findings in fractional order analysis and its applications. The authors—noted experts on the topic—offer an examination of the theory, methods, applications, and the modern tools and techniques in the field of fractional order analysis. The information, tools, and applications presented can help develop mathematical methods and models with better accuracy. Comprehensive in scope, the book covers a range of topics including: new fractional operators, fractional derivatives, fractional differential equations, inequalities for different fractional derivatives and fractional integrals, fractional modeling related to transmission of Malaria, and dynamics of Zika virus with various fractional derivatives, and more. Designed to be an accessible text, several useful, relevant and connected topics can be found in one place, which is crucial for an understanding of the research problems of an applied nature. This book: Contains recent development in fractional calculus Offers a balance of theory, methods, and applications Puts the focus on fractional analysis and its interdisciplinary applications, such as fractional models for biological models Helps make research more relevant to real-life applications Written for researchers, professionals and practitioners, Fractional Order Analysis offers a comprehensive resource to fractional analysis and its many applications as well as information on the newest research.

Author: Charles K. Chui
Publisher: SIAM
ISBN: 9780898719727
Category : Mathematics
Languages : en
Pages : 228

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Book Description
Wavelets continue to be powerful mathematical tools that can be used to solve problems for which the Fourier (spectral) method does not perform well or cannot handle. This book is for engineers, applied mathematicians, and other scientists who want to learn about using wavelets to analyze, process, and synthesize images and signals. Applications are described in detail and there are step-by-step instructions about how to construct and apply wavelets. The only mathematically rigorous monograph written by a mathematician specifically for nonspecialists, it describes the basic concepts of these mathematical techniques, outlines the procedures for using them, compares the performance of various approaches, and provides information for problem solving, putting the reader at the forefront of current research.