This open book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.
This open book is licensed under a Creative Commons License (CC BY). You can download Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 ebook for free in PDF format (21.0 MB).
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018
Science and Mathematics
The book serves both as a reference for
various scaled models with corresponding dimensionless numbers, and as a
resource for learning the art of scaling.
A special feature of the book is the emphasis on how to create software
for scaled models, based on existing software for unscaled models.
Scaling (or non-dimensionalization) is a
This book presents computer programming as a key method for solving mathematical problems. This second edition of the well-received book has been extensively revised: All code is now written in Python version 3.6 (no longer version 2.7). In addition, the two first chapters of the previous edition have been extended and split up into five new chapte...
In this book we discuss several numerical methods for solving ordinary differential equations. We emphasize the aspects that play an important role in practical problems. We conﬁne ourselves to ordinary differential equations with the exception of the last chapter in which we discuss the heat equation, a parabolic partial differential equation. T...
This book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rel...
This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs o...
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