Numerical Approximation of Ordinary Differential Problems: From Deterministic to Stochastic Numerical Methods

This book provides a comprehensive and self-contained introduction to the numerical discretization of ordinary differential equations (ODEs) and stochastic differential equations (SDEs). It is intended for students and instructors,with motivational aspects,historical background,examples,and software programs implemented in Matlab. It also contains portraits of pioneers in the field.

Format: Paperback / softback
Length: 385 pages
Publication date: 26 August 2023
Publisher: Springer International Publishing AG

This comprehensive book delves into the intricate realm of numerical discretization of ordinary differential equations (ODEs), exploring various perspectives and approaches. It begins by focusing on the accurate computation of numerical solutions for deterministic problems, showcasing the importance of achieving precise results. Subsequently, the book takes a modern approach, emphasizing the reproduction of qualitative properties of the continuous problem along the discretized dynamics over extended periods. The journey continues with an exploration of stochastic differential equations (SDEs), aiming to provide valuable tools for generalizing the techniques developed for ODEs to the stochastic context. Additionally, the book addresses numerical issues unique to SDEs, offering insightful insights.

The author's extensive teaching experience and extensive research conducted over the past decade have culminated in this invaluable resource. Designed for students and instructors alike, the book offers a comprehensive and self-contained curriculum, making it suitable for both novice and advanced learners. It includes motivational aspects, historical background, practical examples, and a comprehensive software program implemented in Matlab, which serves as a valuable tool for the laboratory component of courses focused on numerical ODEs/SDEs. Furthermore, the book features portraits of renowned pioneers in the numerical discretization of differential problems, providing a framework for understanding their significant contributions to the field.

In addition to its academic value, this book prioritizes readability, ensuring that complex concepts are presented in a clear and accessible manner. Whether you are a student seeking to deepen your understanding of numerical methods or an instructor looking to enrich your course material, this book is an indispensable resource that will guide you through the intricacies of numerical discretization and its applications.

Weight: 720g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031313424
Edition number: 1st ed. 2023