Overview

This book addresses an important class of mathematical problems (the Riemann problem) for first-order hyperbolic partial differential equations (PDEs), which arise when modeling wave propagation in applications such as fluid dynamics, traffic flow, acoustics, and elasticity. It covers the fundamental ideas related to classical Riemann solutions, including their special structure and the types of waves that arise, as well as the ideas behind fast approximate solvers for the Riemann problem. The emphasis is on the general ideas, but each chapter delves into a particular application. The book is available in electronic form as a collection of Jupyter notebooks that contain executable computer code and interactive figures and animations.

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9781611976205

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David I. Ketcheson is an associate professor of applied mathematics and computational science at King Abdullah University of Science & Technology, Saudi Arabia, and a lead developer of the Clawpack and PyClaw software projects. Randall J. LeVeque is Professor Emeritus of Applied Mathematics at the University of Washington. He is a lead developer of the Clawpack and GeoClaw software packages and the author of several books on numerical methods for differential equations. Mauricio del Razo is a postdoctoral researcher at the Freie Universität Berlin.

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