Wavelet Solutions for Reaction-Diffusion Problems in Science and Engineering

Wavelet Solutions for Reaction-Diffusion Problems in Science and Engineering
Author: G. Hariharan
Publisher:
Total Pages: 177
Release: 2019
Genre: Differential equations
ISBN: 9789813299610

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The book focuses on how to implement discrete wavelet transform methods in order to solve problems of reaction-diffusion equations and fractional-order differential equations that arise when modelling real physical phenomena. It explores the analytical and numerical approximate solutions obtained by wavelet methods for both classical and fractional-order differential equations; provides comprehensive information on the conceptual basis of wavelet theory and its applications; and strikes a sensible balance between mathematical rigour and the practical applications of wavelet theory. The book is divided into 11 chapters, the first three of which are devoted to the mathematical foundations and basics of wavelet theory. The remaining chapters provide wavelet-based numerical methods for linear, nonlinear, and fractional reaction-diffusion problems. Given its scope and format, the book is ideally suited as a text for undergraduate and graduate students of mathematics and engineering.

Wavelet Solutions for Reaction–Diffusion Problems in Science and Engineering

Wavelet Solutions for Reaction–Diffusion Problems in Science and Engineering
Author: G. Hariharan
Publisher: Springer Nature
Total Pages: 177
Release: 2019-09-17
Genre: Mathematics
ISBN: 9813299606

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The book focuses on how to implement discrete wavelet transform methods in order to solve problems of reaction–diffusion equations and fractional-order differential equations that arise when modelling real physical phenomena. It explores the analytical and numerical approximate solutions obtained by wavelet methods for both classical and fractional-order differential equations; provides comprehensive information on the conceptual basis of wavelet theory and its applications; and strikes a sensible balance between mathematical rigour and the practical applications of wavelet theory. The book is divided into 11 chapters, the first three of which are devoted to the mathematical foundations and basics of wavelet theory. The remaining chapters provide wavelet-based numerical methods for linear, nonlinear, and fractional reaction–diffusion problems. Given its scope and format, the book is ideally suited as a text for undergraduate and graduate students of mathematics and engineering.

Wavelet Theory

Wavelet Theory
Author: Somayeh Mohammady
Publisher: BoD – Books on Demand
Total Pages: 399
Release: 2021-02-24
Genre: Mathematics
ISBN: 1838819479

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The wavelet is a powerful mathematical tool that plays an important role in science and technology. This book looks at some of the most creative and popular applications of wavelets including biomedical signal processing, image processing, communication signal processing, Internet of Things (IoT), acoustical signal processing, financial market data analysis, energy and power management, and COVID-19 pandemic measurements and calculations. The editor’s personal interest is the application of wavelet transform to identify time domain changes on signals and corresponding frequency components and in improving power amplifier behavior.

Ubiquitous Computing and Ambient Intelligence. Sensing, Processing, and Using Environmental Information

Ubiquitous Computing and Ambient Intelligence. Sensing, Processing, and Using Environmental Information
Author: Juan M. García-Chamizo
Publisher: Springer
Total Pages: 507
Release: 2015-12-12
Genre: Computers
ISBN: 331926401X

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This book constitutes the refereed proceedings of the 9th International Conference on Ubiquitous Computing and Ambient Intelligence, UCAmI 2015, held in Puerto Varas, Chile, in December 2015. The 36 full papers presented together with 11 short papers were carefully reviewed and selected from 62 submissions. The papers are grouped in topical sections on adding intelligence for environment adaption; ambient intelligence for transport; human interaction and ambient intelligence; and ambient intelligence for urban areas.

Fourier Methods in Science and Engineering

Fourier Methods in Science and Engineering
Author: Wen Li
Publisher: CRC Press
Total Pages: 341
Release: 2022-11-21
Genre: Technology & Engineering
ISBN: 1000781089

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This innovative book discusses and applies the generalized Fourier Series to a variety of problems commonly encountered within science and engineering, equipping the readers with a clear pathway through which to use the Fourier methods as a solution technique for a wide range of differential equations and boundary value problems. Beginning with an overview of the conventional Fourier series theory, this book introduces the generalized Fourier series (GFS), emphasizing its notable rate of convergence when compared to the conventional Fourier series expansions. After systematically presenting the GFS as a powerful and unified solution method for ordinary differential equations and partial differential equations, this book expands on some representative boundary value problems, diving into their multiscale characteristics. This book will provide readers with the comprehensive foundation necessary for solving a wide spectrum of mathematical problems key to practical applications. It will also be of interest to researchers, engineers, and college students in various science, engineering, and mathematics fields.

Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations

Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations
Author: Santanu Saha Ray
Publisher: CRC Press
Total Pages: 212
Release: 2018-01-12
Genre: Mathematics
ISBN: 1351682210

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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.

Wavelets

Wavelets
Author: Gordon Erlebacher
Publisher: Oxford University Press
Total Pages: 524
Release: 1996-01-04
Genre: Science
ISBN: 0198025424

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Wavelets are spatially localized functions whose amplitude drops off exponentially outside a small "window". They are used to magnify experimental or numerical data and have become powerful tools in signal processing and other computational sciences. This book gives scientists and engineers a practical understanding of wavelets--their origins, their purpose, their use, and their prospects. It covers the applications of wavelets as a diagnostic tool and the use of wavelet basis functions to solve differential equations. Each chapter was written by one of five lecturers of a course sponsored by the Institute of Computer Applications in Science and Engineering (ICASE) and the NASA Langley Research Center. Not only does this book treat the latest advances on the subject, but it also attempts to impart practical knowledge to allow scientists and engineers to evaluate objectively where these tools stand in relation to their needs.

Wavelet Applications in Chemical Engineering

Wavelet Applications in Chemical Engineering
Author: Rodolphe L. Motard
Publisher: Springer
Total Pages: 350
Release: 1994-07-31
Genre: Mathematics
ISBN:

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Increasing emphasis on safety, productivity and quality control has provided an impetus to research on better methodologies for fault diagnosis, modeling, identification, control and optimization ofchemical process systems. One of the biggest challenges facing the research community is the processing of raw sensordata into meaningful information. Wavelet analysis is an emerging field of mathematics that has provided new tools and algorithms suited for the type of problems encountered in process monitoring and control. The concept emerged in the geophysical field as a result ofthe need for time-frequency analytical techniques. It has since been picked up by mathematicians and recognized as a unifying theory for many ofthe methodologies employed in the past in physics and signal processing. l Meyer states: "Wavelets are without doubt an exciting and intuitive concept. The concept brings with it a new way of thinking, which is absolutely essential and was entirely missing in previously existing algorithms. " The unification ofthe theory from these disciplines has led to applications of wavelet transforms in many areas ofscience and engineering including: • pattern recognition • signal analysis • time-frequency decomposition • process signal characterization and representation • process system modeling and identification • control system design, analysis and implementation • numerical solution ofdifferential equations • matrix manipulation About a year ago, in talking to various colleagues and co-workers, it became clear that a number of chemical engineers were fascinated with this new concept.

Advanced Petroleum Reservoir Simulation

Advanced Petroleum Reservoir Simulation
Author: M. R. Islam
Publisher: John Wiley & Sons
Total Pages: 592
Release: 2016-08-11
Genre: Technology & Engineering
ISBN: 1119038715

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This second edition of the original volume adds significant new innovations for revolutionizing the processes and methods used in petroleum reservoir simulations. With the advent of shale drilling, hydraulic fracturing, and underbalanced drilling has come a virtual renaissance of scientific methodologies in the oil and gas industry. New ways of thinking are being pioneered, and Dr. Islam and his team have, for years now, been at the forefront of these important changes. This book clarifies the underlying mathematics and physics behind reservoir simulation and makes it easy to have a range of simulation results along with their respective probability. This makes the risk analysis based on knowledge rather than guess work. The book offers by far the strongest tool for engineers and managers to back up reservoir simulation predictions with real science. The book adds transparency and ease to the process of reservoir simulation in way never witnessed before. Finally, No other book provides readers complete access to the 3D, 3-phase reservoir simulation software that is available with this text. A must-have for any reservoir engineer or petroleum engineer working upstream, whether in exploration, drilling, or production, this text is also a valuable textbook for advanced students and graduate students in petroleum or chemical engineering departments.

Integral Methods in Science and Engineering

Integral Methods in Science and Engineering
Author: Barbara S Bertram
Publisher: CRC Press
Total Pages: 371
Release: 2019-05-20
Genre: Mathematics
ISBN: 1420036033

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Based on proceedings of the International Conference on Integral Methods in Science and Engineering, this collection of papers addresses the solution of mathematical problems by integral methods in conjunction with approximation schemes from various physical domains. Topics and applications include: wavelet expansions, reaction-diffusion systems, variational methods , fracture theory, boundary value problems at resonance, micromechanics, fluid mechanics, combustion problems, nonlinear problems, elasticity theory, and plates and shells.