5 Best Books on Numerical Methods for Conservation Laws

We have compiled a list of the Best Reference Books on Numerical Methods For Conservation Laws, which are used by students of top universities, and colleges. This will help you choose the right book depending on if you are a beginner or an expert. Here is the complete list of Numerical Methods For Conservation Laws Books with their authors, publishers, and an unbiased review of them as well as links to the Amazon website to directly purchase them. If permissible, you can also download the free PDF books on Numerical Methods For Conservation Laws below.

1."Numerical Methods for Conservation Laws" by Leveque R J “Numerical Methods for Conservation Laws” Book Review: This book provides an introduction to the development of a numerical method for conservation laws. It covers various topics such as the derivation of conservation laws, scalar conservation laws, examples of scalar laws, as well as nonlinear and linear hyperbolic systems. Other chapters discuss topics like shocks and the Hugoniot locus, refraction waves, integral curves, the Riemann problem for the Euler equations, and computing discontinuous solutions. Each chapter includes exercises and references for further study. This book is particularly relevant for students of applied physics.
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2."An Introduction to Recent Developments in Theory and Numerics for Conservation Laws" by Dietmar Kröner and Mario Ohlberger “An Introduction to Recent Developments in Theory and Numerics for Conservation Laws” Book Review: The core concepts of computational field dynamics are clearly defined in this book. The main chapters delve into topics such as the kinetic scheme for gas dynamics, the entropy inequality for kinetic schemes, non-classical shock of systems of conservation laws, and numerical methods for gas dynamics systems on unstructured meshes. The book covers other relevant topics such as viscosity and relaxation approximation for hyperbolic systems of conservation laws, a posteriori analysis, and adaptivity for finite elements. Throughout the book, equations are explained in detail to ensure clarity. This book is a valuable resource for students of applied mathematics and physics.
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3."Front Tracking for Hyperbolic Conservation Laws (Applied Mathematical Sciences" by H Holden and Nils Henrik Risebro “Front Tracking for Hyperbolic Conservation Laws (Applied Mathematical Sciences” Book Review: This book offers an introduction to the fundamental concepts of the theory of hyperbolic conservation laws. The main chapters cover dependent flux functions, the Riemann problem for the Euler equations, and the theory of partial differential equations. Additionally, the book includes other relevant topics such as the multidimensional scalar case, front tracking, and finite differences. Detailed examples and equations are provided throughout the book to enhance comprehension. This book is an excellent resource for students of applied mathematics and physics.
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4."Numerical Partial Differential Equations: Conservation Laws and Elliptic Equations" by J W Thomas “Numerical Partial Differential Equations: Conservation Laws and Elliptic Equations” Book Review: This book provides explanation of partial differential equations. The main topics covered include the stability of initial-boundary-value schemes, conservation laws, elliptic equations, and handling irregular regions and grids. To facilitate learning, fully worked-out problems are included for practice. The book is primarily designed for graduate students of applied mathematics and engineering.
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5."Analysis and Numerics for Conservation Laws" by Gerald Warnecke “Analysis and Numerics for Conservation Laws” Book Review: This book presents the fundamental concepts of numerics for conservation laws. The book covers a range of topics, including numeric for magnetoplasmadynamic propulsion, hexagonal kinetic models, numerical simulation of kinetic boundary layers, and high-resolution simulation of detonations with detailed chemistry. Other topics include simulation of solar radiative magneto-convection, radiation magnetohydrodynamics, and hyperbolic systems. The book includes 236 figures and 18 tables to aid understanding, and it provides in-depth descriptions of 22 chapters. This book is an ideal resource for students studying astrophysics, applied mathematics, physics, and engineering.
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