Mathematics

Research Notes on Computing and Communication Sciences

Solving Differential Equations
A Computational Approach

Editors: Geeta Arora, PhD
Firdous Ahmad Shah, PhD

Solving Differential Equations

In production
Pub Date: Forthcoming June 2026
Hardback Price: $190 USD | £150 UK
Hard ISBN: 9781779644442
E-Book ISBN: 9781779644459
Pages: est. 210pp w index
Binding Type: Hardback / ebook
Series: Research Notes on Computing and Communication Sciences
Notes: 17 color and 115 b/w illustrations


Reviews
“A valuable tool for anyone interested in the computational solution of differential equations and its diverse applications. Offer[s] not only theoretical insights but also practical implementations and comparative studies, making this volume a valuable resource for both researchers and practitioners . . . A timely and comprehensive overview of this dynamic and essential field. It is a valuable contribution to the literature and a testament to the ongoing advancements in computational mathematics and its applications.”
—From the Foreword by Dr. Pinkey Chauhan, Assistant Professor, Indira Gandhi National Open University, India

The study of differential equations lies at the heart of numerous scientific and engineering disciplines. From modeling the intricate dynamics of physical systems to simulating complex ecological interactions, differential equations provide the mathematical framework for understanding and predicting change. However, many real-world problems give rise to equations that defy analytical solutions, necessitating the development and application of sophisticated computational techniques. This new book, Solving Differential Equations: A Computational Approach, addresses this crucial need by presenting a diverse collection of cutting-edge numerical and semi-analytical methods for tackling a wide range of differential equation problems.

The book first focuses on computational approaches for general differential equations, showcasing a variety of powerful techniques. Readers will find explorations of globally convergent schemes for nonlinear engineering problems, implementations of the reduced differential transform method for Schrödinger equations, and high-order finite difference methods for reaction-diffusion equations. A discussion of homotopy perturbation methods for wave-type equations, highlighting their graphical representations, is included.

The book then shifts its focus to the application of computational methods in the specific context of mathematical ecology. Chapters demonstrate the power of these techniques in understanding complex ecological systems, underscoring the practical relevance of computational methods in addressing real-world ecological challenges.

The contributions within this book represent the work of leading researchers in their respective fields. The chapters offer not only theoretical insights but also practical implementations and comparative studies, making this volume a valuable resource for both researchers and practitioners. Whether you are a student seeking to deepen your understanding of computational methods or a seasoned researcher looking for advanced techniques, Solving Differential Equations: A Computational Approach provides a timely and comprehensive overview of this dynamic and essential field.

CONTENTS:
Foreword by Dr. Pinkey Chauhan

Preface

1. On Globally Convergent Schemes for Nonlinear Problems in Engineering
Mudassir Shams, Nasreen Kausar, and Seyyed Ahmad Edalatpana

2. Implementation of a Reduced Differential Transform Method on Schrödinger Equations
Mamta Kapoor, Navdeep Singh, and Geeta Arora

3. Sixth-Order Compact Finite Difference Method with an SSP-RK43 Scheme for a Numerical Solution of Fisher’s Reaction-Diffusion Equation
Ravneet Kaur, Shallu, Geeta Arora, Gurhan Gurarslan, and V. K. Kukreja

4. A Semi-Analytic Method for Solving Nonlinear Systems of Partial Differential Equations via the Method of Lines by Reproducing the Kernel Hilbert Space Method
Gautam Patel and Kaushal Patel

5. Solution of Fractional Advection-Dispersion Equations Using an Homotopy Analysis Method: A Comparative Study
Amit Kumar Pandey

6. Numerical Solution of a Spin Wave Transport Equation
E. V. Reshetova, S. Li, and O. V. Kravchenko

7. Solution of Wave Type Equations by Using a Homotopy Perturbation Method and Their Graphical Representation
Dharmendra Kumar Singh and Shubhi Saxena

8. An Analytic Study of the Prey-Predator Food Chain Model
Shiv Raj and Ahmed Ali Mohsen

9. Single-Type Population Models in Mathematical Ecology
Mahmood Khalid Jasim, Sunil Kumar Maurya, Sara Hossein Zergani, Abdulrahman Ali Al Maqbali, and Geeta Arora

10. Stability Analysis of the Three Species Model Using the Holling Type II Functional Response
Divya B. and Kavitha K.

11. Modeling Effect of Soil Pollution on Root-Shoot Biomass
Preety Kalra, Shreya Tangri, O. P. Misra, and Wan Zuki Azman Wan Muhamad

Index


About the Authors / Editors:
Editors: Geeta Arora, PhD
Professor, Department of Mathematics, Lovely Professional University, Punjab, India

Geeta Arora, PhD, has over 12 years of teaching experience and is working as a Professor in the Department of Mathematics at Lovely Professional University, Punjab, India. She has published around 70 research papers (Scopus-indexed) in both international and national journals. She has also authored 15 book chapters in national and international publications and written a book on Vedic Mathematics and a book on Essential Statistics. She has also edited books on numerical methods with Taylor & Francis and IGI Global. She has published eight books with national publisher along with five ongoing books with national and international publishers. Her area of research is the development of numerical methods and statistics. She received research appreciation awards in 2017, 2019, and 2024 from Lovely Professional University. She has conducted several workshops on MATLAB and Vedic mathematics for students and faculty members within and outside the university campus. She has supervised nine PhD scholars and is currently guiding six PhD scholars. Dr. Arora earned her PhD degree from IIT Roorkee, India.

Firdous Ahmad Shah, PhD
Associate Professor, Department of Mathematics, University of Kashmir, South Campus, Anantnag, Jammu and Kashmir, India

Firdous Ahmad Shah, PhD, is an accomplished mathematician and Associate Professor at the Department of Mathematics, University of Kashmir, India. With a robust publication record of over 180 articles, Dr. Shah has made substantial strides in the field of mathematics, particularly in the realm of wavelet transforms. His work spans a diverse range of applications, showcased in his authored and co-authored books published by publishers such as CRC Press and Springer. Dr. Shahs influence extends beyond publications, as he has actively participated in numerous short-term courses and conferences, fostering knowledge dissemination. A member of various societies, Dr. Shahs dedication to advancing mathematical research is underscored by his involvement in six funded projects by the Indian Department of Science and Technology (DST). He has guided eight scholars, nurturing the next generation of mathematicians. Dr. Shah serves on the editorial board of 35 reputes journals.




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