The book focuses on how to implement discrete wavelet transform methods in order to solve problems of reactiondiffusion 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 reactiondiffusion problems. Given its scope and format, the book is ideally suited as a text for undergraduate and graduate students ofmathematics and engineering.

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

Autorentext

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.

Klappentext

1. Reaction-Diffusion Problems.- 2. Wavelet Analysis - An Overview.- 3. Shifted Chebyshev Wavelets and Shifted Legendre Wavelets - Preliminaries.- 4. Wavelet Method to Film-Pore Diffusion Model for Methylene Blue Adsorption onto Plant Leaf Powders.- 5. An Efficient Wavelet-based Spectral Method to Singular Boundary Value Problems.- 6. Analytical Expressions of Amperometric Enzyme Kinetics Pertaining to the Substrate Concentration using Wavelets.- 7 Haar Wavelet Method for Solving Some Nonlinear Parabolic Equations.- 8. An Efficient Wavelet-based Approximation Method to Gene Propagation Model Arising in Population Biology.- 9. Two Reliable Wavelet Methods for Fitzhugh-Nagumo (FN) and Fractional FN Equations.- 10. A New Coupled Wavelet-based Method Applied to the Nonlinear Reaction-Diffusion Equation Arising in Mathematical Chemistry.- 11. Wavelet based Analytical Expressions to Steady State Biofilm Model Arising in Biochemical Engineering.

   Inhalt

   1. Reaction-Diffusion Problems.- 2. Wavelet Analysis An Overview.- 3. Shifted Chebyshev Wavelets and Shifted Legendre Wavelets Preliminaries.- 4. Wavelet Method to Film-Pore Diffusion Model for Methylene Blue Adsorption onto Plant Leaf Powders.- 5. An Efficient Wavelet-based Spectral Method to Singular Boundary Value Problems.- 6. Analytical Expressions of Amperometric Enzyme Kinetics Pertaining to the Substrate Concentration using Wavelets.- 7 Haar Wavelet Method for Solving Some Nonlinear Parabolic Equations.- 8. An Efficient Wavelet-based Approximation Method to Gene Propagation Model Arising in Population Biology.- 9. Two Reliable Wavelet Methods for Fitzhugh-Nagumo (FN) and Fractional FN Equations.- 10. A New Coupled Wavelet-based Method Applied to the Nonlinear Reaction-Diffusion Equation Arising in Mathematical Chemistry.- 11. Wavelet based Analytical Expressions to Steady State Biofilm Model Arising in Biochemical Engineering.