Numerical Methods for Ordinary Differential Equations: Initial Value Problems - Griffiths, Higham

[Completed]

This is an exceptional resource for those who want to start learning about the numerical methods used to solve IVPs. Authors adopt a step-by-step approach, explaining new ideas and providing numerous examples and simulations to illustrate the concepts. Mathematical complexities are kept to a minimum making it easy to grasp the fundamental concepts. I particularly enjoyed reading the chapters on geometric integration of Hamiltonian systems for long-term simulations; specialized methods designed to preserve system invariants. Overall, this book is a great starting point to learn about the subject. I truely enjoyed it!

PoW

Computer methods for ordinary differential equations and differential-algebraic equations - Ascher, Petzold

[Reading]

This book is quite unique. On one hand, it covers a wide range of interesting ideas; on the other, there are a lot of places in the book where the authors introduce concepts without providing immediate explanations, challenging the reader to persevere and think critically. This book demands active engagement and a willingness to refer to external resources to grasp the more complex ideas. Compared to the previous title (1), it provides a more in-depth analysis of the subject matter using more sophisticated mathematics. End-of-chapter exercises aim to engage the reader by introducing new concepts that were not discussed in the main content of the chapter.