Integral and Integro-Differential Equations: Wavelet-Based Numerical Methods

This book provides a comprehensive study of numerical techniques for solving integral and integro-differential equations using wavelet-based approximation methods. It combines both theoretical insights and practical applications, focusing on integer- and fractional-order equations, including those with weakly singular kernels. Starting with key definitions and theorems from integral equations and fractional calculus, the book establishes a clear mathematical framework. It then introduces wavelet-based schemes for approximating solutions, with a particular focus on convergence, stability, and error analysis. Each chapter is enriched with numerical examples, graphs, and tables that demonstrate the accuracy and computational efficiency of the proposed methods.

• Employs wavelet approximation methods to solve a wide range of integral and integro-differential equations
• Expands the scope of applicable equations by covering both classical and fractional-order models
• Illustrates the effectiveness of wavelet methods in handling weakly singular kernels through worked-out examples
• Provides rigorous theoretical validation for the accuracy and reliability of each method.

This book is intended for postgraduate students, researchers, and professionals in mathematics, engineering, and applied sciences who seek modern computational techniques for solving integral and integro-differential equations.

Santanu Saha Ray is currently a Professor in the Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, India. He was also a professor and former Head of the Department of Mathematics, National Institute of Technology, Rourkela, India. He was elected Fellow of the Institute of Mathematics and Its Applications, United Kingdom, in 2018. Dr. Saha Ray is enlisted in the list of "WORLD RANKING OF TOP 2% SCIENTISTS" from India as per a subject-wise analysis conducted by a team of scientists at Stanford University, led by Dr. John PA Ioannidis. Recently, he was elected for Full Membership in Sigma Xi, The Scientific Research Honour Society, USA. Dr. Saha Ray has more than 23 years of teaching experience at the undergraduate and postgraduate levels in National Institute of Technology, Rourkela and two private Engineering Institutes in Kolkata, West Bengal. He has more 22 years of research experience in various fields of Applied Mathematics. He has published many peer-reviewed research papers in numerous fields and various international SCI journals of repute. He was awarded an IOP Publishing Top Cited Author Award 2018 from India in the field of Physics, published across the whole IOP Publishing portfolio, for the three years (2015 to 2017), using citations recorded in Web of Science. He has contributed papers on several topics, such as fractional calculus, mathematical modelling, mathematical physics, stochastic modeling, integral equations, and wavelet methods.

Srikanta Behera is an assistant professor in the Department of Mathematics, Kalinga Institute of Industrial Technology (KIIT), Bhubaneswar, Odisha, India. Dr. Behera obtained his PhD in 2022 from National Institute of Technology, Rourkela, Odisha, India and M.Sc. (Master of Science) degree in 2015 from Maharaja Sriram Chandra Bhanja Deo University (North Orissa University), Baripada, Odisha, India. He completed his B.Sc. (Bachelor of Science) degree in mathematics (honors) at Gangadhar Meher Autonomous College (Sambalpur University), Sambalpur, Odisha, India, in 2013. Dr. Behera has 6 years of teaching experience at the undergraduate and postgraduate levels. He has also about 7 years of research experience in various fields of applied mathematics. He has published 12 research papers in numerous fields and various international SCI journals of repute, including Applied Mathematics and Computation, Journal of Computational and Applied Mathematics, Computational and Applied Mathematics, Mathematics and Computers in Simulation, Mediterranean Journal of Mathematics, Engineering Computations, Iranian Journal of Science and Technology, Transactions A Science, Mathematical Methods in the Applied Sciences. He has contributed papers on several topics, such as fractional calculus, numerical solution of integral and integro-differential equations, and wavelet methods.