Wavelet Solutions for Reaction–Diffusion Problems in Science and Engineering

Beschreibung

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.
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.
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

Autor*in

G. Hariharan

Themen in »Wavelet Solutions for Reaction–Diffusion Problems in Science and Engineering«

Haar Wavelets Legendre Wavelets Operational Matrices Chebyshev Wavelets Differential Equations ordinary differential equations partial differential equations

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“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)

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