Wavelet Solutions for Reaction–Diffusion Problems in Science and Engineering

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.

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.