This book offers a comprehensive and accessible introduction to the fundamental theory of finite difference schemes used in the numerical solution of partial differential equations. Originally published in 1989, it aims to clearly present the essential methods required to implement finite difference schemes and to deepen understanding of the underlying theoretical principles.
One of the few texts in its field to rigorously and clearly address the theory of stability, this book also explores the theory of initial-boundary value problems in relation to finite difference schemes. Its thorough treatment makes it an invaluable resource for students and practitioners seeking a solid foundation in this area.
In this updated edition, the concept of a stability domain has been incorporated into the definition of stability and is emphasized throughout the text. The author has also enhanced the book with numerous new figures and tables designed to clarify key concepts and illustrate the properties of finite difference schemes, making complex ideas more accessible and visually understandable.