Integral and Integro-Differential Equations: Wavelet-Based Numerical Methods
暫譯: 積分與積分微分方程：基於小波的數值方法

Ray, Santanu Saha, Behera, Srikanta

Integral and Integro-Differential Equations: Wavelet-Based Numerical Methods
  • 出版商: CRC
  • 出版日期: 2025-12-04
  • 售價: $7,870
  • 貴賓價: 9.5 折 $7,477
  • 語言: 英文
  • 頁數: 356
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 1032586125
  • ISBN-13: 9781032586120
  • 相關分類: 數值分析 Numerical-analysis

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商品描述

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.

Features

  • 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.

商品描述(中文翻譯)

這本書提供了一個全面的數值技術研究，旨在使用基於小波的近似方法來解決積分和積分微分方程。它結合了理論見解和實際應用，專注於整數和分數階方程，包括那些具有弱奇異核的方程。書中首先介紹了積分方程和分數微積分的關鍵定義和定理，建立了一個清晰的數學框架。接著，書中引入了基於小波的方案來近似解，特別關注收斂性、穩定性和誤差分析。每一章都配有數值範例、圖表和表格，展示所提方法的準確性和計算效率。

特色
- 採用小波近似方法解決各種積分和積分微分方程
- 通過涵蓋經典和分數階模型擴展適用方程的範圍
- 通過具體範例說明小波方法在處理弱奇異核方面的有效性
- 提供每種方法準確性和可靠性的嚴謹理論驗證

本書適合研究生、研究人員以及數學、工程和應用科學領域的專業人士，尋求現代計算技術以解決積分和積分微分方程。

作者簡介

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 than 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.

作者簡介(中文翻譯)

Santanu Saha Ray 目前是印度西孟加拉邦 Shibpur 的印度工程科學與技術學院數學系教授。他曾擔任印度 Rourkela 國立技術學院數學系教授及系主任。2018 年，他被選為英國數學及其應用學會的院士。根據斯坦福大學約翰·PA·伊奧安尼迪斯博士領導的科學家團隊進行的學科分析，Dr. Saha Ray 被列入印度「世界前 2% 科學家排名」名單。最近，他被選為美國 Sigma Xi 科學研究榮譽學會的正式會員。Dr. Saha Ray 在 Rourkela 國立技術學院及西孟加拉邦 Kolkata 的兩所私立工程學院擁有超過 23 年的本科及研究生教學經驗。他在應用數學的各個領域擁有超過 22 年的研究經驗。他在多個領域及各種國際知名的 SCI 期刊上發表了許多經過同行評審的研究論文。他因在物理學領域的貢獻，獲得了 2018 年印度 IOP 出版社的高引用作者獎，該獎項涵蓋了整個 IOP 出版社的作品，基於 2015 至 2017 年間在 Web of Science 記錄的引用數據。他在多個主題上發表了論文，如分數微積分、數學建模、數學物理、隨機建模、積分方程和小波方法。

Srikanta Behera 是印度奧里薩邦 Bhubaneswar 的 Kalinga 工業技術學院 (KIIT) 數學系助理教授。Dr. Behera 於 2022 年在印度 Rourkela 國立技術學院獲得博士學位，並於 2015 年在印度奧里薩邦 Baripada 的 Maharaja Sriram Chandra Bhanja Deo 大學（北奧里薩大學）獲得碩士學位 (M.Sc.)。他於 2013 年在印度奧里薩邦 Sambalpur 的 Gangadhar Meher 自治學院（Sambalpur 大學）獲得數學（榮譽）學士學位 (B.Sc.)。Dr. Behera 擁有 6 年的本科及研究生教學經驗，並在應用數學的各個領域擁有約 7 年的研究經驗。他在多個領域及各種國際知名的 SCI 期刊上發表了 12 篇研究論文，包括 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。他在多個主題上發表了論文，如分數微積分、積分及積分微分方程的數值解法和小波方法。

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