On a Class of High Resolution Total-Variation-Stable Finite-Difference Schemes (Classic Reprint) - Tapa blanda

Sinopsis

High-resolution TVD finite-difference schemes for nonlinear conservation laws. Learn how to build numerical methods that are stable, accurate, and capable of handling shocks and discontinuities in hyperbolic systems.


This book presents a clear path from the theory of conservation laws to practical schemes. It explains how total-variation stability, entropy considerations, and convergence ideas come together to produce robust numerical methods. The discussion covers first-order TVD schemes, then advances to second-order accuracy, and extends the ideas to systems of equations and steady-state calculations. The methods balance dissipation and accuracy, aiming to capture essential features of the solution without spurious oscillations.


- Grounding in the convergence framework for finite-difference approximations of conservation laws
- Design principles that couple consistency with the conservation law and its entropy inequality to ensure convergence
- Techniques to achieve second-order accuracy while preserving TVD properties
- Extensions to systems of equations and practical considerations for steady-state computations

Ideal for researchers, graduate students, and practitioners who work on numerical methods for partial differential equations and computational fluid dynamics.
Ideal for readers of advanced numerical analysis and computational physics texts seeking rigorous, applicable guidance on high-resolution schemes.

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