Collocation Approach with B-spline Basis Functions using MATLAB

1. Auflage 2027
ISBN: 978-87-438-1225-8
Verlag: Taylor & Francis

Buch, Englisch, 186 Seiten, Format (B × H): 156 mm x 234 mm

Reihe: River Publishers Series in Mathematical, Statistical and Computational Modelling for Engineering

This book provides a practical and accessible introduction to the collocation method with B-spline basis functions using MATLAB, offering a clear and powerful approach to solving a wide range of differential equations in science and engineering. It demystifies the technique through intuitive explanations and hands-on implementation, guiding the reader from foundational concepts—such as B-splines and the MATLAB environment—to more advanced, application-driven topics.

Step-by-step chapters illustrate how to solve specific types of equations, including detailed methodologies for constructing numerical schemes, forming matrices, applying boundary and initial conditions, and using the Thomas algorithm. Comprehensive case studies feature Fisher’s equation, Burgers’ equation, and the coupled Burgers’ equation, accompanied by complete MATLAB codes that can be directly executed, modified, and visualized through figures and tables.

The book concludes by showcasing the flexibility of the method through variations such as trigonometric B-splines. Designed for students, researchers, and professionals, this resource equips readers with the confidence and tools needed to apply B-spline collocation techniques effectively to real-world computational problems.

Zielgruppe

Academic, Postgraduate, and Professional Practice & Development

Autoren/Hrsg.

Arora, Geeta

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

1. Introduction 2. Solving Fisher's Equation by the Collocation Method 3. Solving Burger's Equation by the Collocation Method 4. Solving Coupled Burger's Equation by the Collocation Method 5. Forms of B-spline Basis Functions

Über Autor(innen)

Dr. Geeta Arora earned her Ph.D. degree from IIT Roorkee, India in 2011. She is working as a Professor in the Department of Mathematics at Lovely Professional University, Punjab, India. She has over twelve years of teaching experience and published around 90 research papers (Scopus Indexed) in both international and national Journals. She has authored 15 book chapters in national and international publications. Also, she has written a book on Vedic Mathematics and a book on Essential Statistics. She has also edited three international books on numerical methods for Taylor Francis, Elsevier and IGI Global and is currently working on many books with AAP Taylor Francis, De Gruyters, Wiley Scrivener and River publishers. Her area of research is the development of numerical methods and statistics. She received a research appreciation award in 2017, 2019 and 2024 from Lovely Professional University, Punjab, India. 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 Ph.D. scholars and is currently guiding six Ph.D. Scholars.