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Wavelet Solutions for Reaction–Diffusion Problems in Science and Engineering

  • Book
  • © 2019

Overview

Authors:
  1. G. Hariharan

    1. School of Arts Science and Humanities (SASH), SASTRA Deemed to be University, Thanjavur, India

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  • Focuses on major applications of recently developed wavelet tools in solving differential equations in engineering
  • Explains how to solve nonlinear differential equations by using wavelet methods like Haar, Legendre, and Chebyshev wavelets
  • Compares the power of the manageable wavelet methods with other numerical methods

Part of the book series: Forum for Interdisciplinary Mathematics (FFIM)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xix
    Download chapter PDF

  2. Reaction–Diffusion (RD) Problems

    • G. Hariharan
    Pages 1-14

  3. Wavelet Analysis—An Overview

    • G. Hariharan
    Pages 15-31

  4. Shifted Chebyshev Wavelets and Shifted Legendre Wavelets—Preliminaries

    • G. Hariharan
    Pages 33-50

  5. Wavelet Method to Film–Pore Diffusion Model for Methylene Blue Adsorption onto Plant Leaf Powders

    • G. Hariharan
    Pages 51-61

  6. An Efficient Wavelet-Based Spectral Method to Singular Boundary Value Problems

    • G. Hariharan
    Pages 63-91

  7. Analytical Expressions of Amperometric Enzyme Kinetics Pertaining to the Substrate Concentration Using Wavelets

    • G. Hariharan
    Pages 93-102

  8. Haar Wavelet Method for Solving Some Nonlinear Parabolic Equations

    • G. Hariharan
    Pages 103-117

  9. An Efficient Wavelet-Based Approximation Method to Gene Propagation Model Arising in Population Biology

    • G. Hariharan
    Pages 119-134

  10. Two Reliable Wavelet Methods to Fitzhugh–Nagumo (FN) and Fractional FN Equations

    • G. Hariharan
    Pages 135-146

  11. A New Coupled Wavelet-Based Method Applied to the Nonlinear Reaction–Diffusion Equation Arising in Mathematical Chemistry

    • G. Hariharan
    Pages 147-161

  12. Wavelet-Based Analytical Expressions to Steady-State Biofilm Model Arising in Biochemical Engineering

    • G. Hariharan
    Pages 163-177
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Keywords

About this book

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 ofmathematics and engineering.

Reviews

“The book is written for graduate students and researchers working in the field of applied mathematics, physics, engineering, and related disciplines with the desideratum to scrutinate the efficiency of employing various wavelet methods in problems of certain partial differential equations.” (Nikhil Khanna, zbMATH 1432.42001, 2020)

Authors and Affiliations

  • School of Arts Science and Humanities (SASH), SASTRA Deemed to be University, Thanjavur, India

    G. Hariharan

About the author

G. Hariharan has been a Senior Assistant Professor at the Department of Mathematics, SASTRA University, Thanjavur, Tamil Nadu, India, since 2003. He previously served as a lecturer at Adhiparasakthi Engineering College, Melmaruvathur, Tamil Nadu. Dr Hariharan received his MSc and PhD degrees in Mathematics from Bharathidasan University, Trichy, and SASTRA University, in 1999 and 2010, respectively. He has over 20 years of teaching experience at the undergraduate and graduate levels at several educational institutions and engineering institutes, as well as 16 years of research experience in applied mathematics. He is a life member of the Indian Society for Technical Education (ISTE), Ramanujan Mathematical Society (RMS), International Association of Engineers (IAENG), and the Indian Society of Structural Engineers (ISSE).
 Dr Hariharan has served as the Principal Investigator of projects for e.g. the DRDO-NRB (Naval Research Board) and Government of India, andhas contributed research papers on several interdisciplinary topics such as wavelet methods, mathematical modelling, fractional calculus, enzyme kinetics, ship dynamics, and population dynamics. He has published over 85 peer-reviewed research papers on differential equations and applications in various leading international journals, including: Applied Mathematics and Computation, Electrochimica Acta, Ocean Engineering, Journal of Computational and Nonlinear Dynamics, MATCH-Communications in Mathematical and Computer Chemistry, Aerospace and Space Sciences, and the Arabian Journal for Science and Engineering. In addition, Dr Hariharan serves on the editorial boards of several prominent journals, including: Communications in Numerical Analysis, International Journal of Modern Mathematical Sciences, International Journal of Computer Applications, and International Journal of Bioinformatics.

Bibliographic Information

  • Book Title: Wavelet Solutions for Reaction–Diffusion Problems in Science and Engineering

  • Authors: G. Hariharan

  • Series Title: Forum for Interdisciplinary Mathematics

  • DOI: https://doi.org/10.1007/978-981-32-9960-3

  • Publisher: Springer Singapore

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2019

  • Hardcover ISBN: 978-981-32-9959-7Published: 27 September 2019

  • Softcover ISBN: 978-981-32-9962-7Published: 28 September 2020

  • eBook ISBN: 978-981-32-9960-3Published: 17 September 2019

  • Series ISSN: 2364-6748

  • Series E-ISSN: 2364-6756

  • Edition Number: 1

  • Number of Pages: XIX, 177

  • Number of Illustrations: 2 b/w illustrations, 25 illustrations in colour

  • Topics: Ordinary Differential Equations, Fourier Analysis, Partial Differential Equations

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