A practical guide to sharp, reliable simulations of wave-like problems. This book presents numerical methods for hyperbolic conservation laws, focusing on how to replace exact Riemann solvers with accurate, efficient approximations while keeping the benefits of Glimm’s approach. It explains the random choice method, entropy conditions, and convergence, with clear paths to applying these ideas to real problems.

- Learn how piecewise-constant approximations and random sampling can produce solutions that sharply resolve shocks and discontinuities.
- Understand how entropy concepts guide stable, physically meaningful results in both theory and practice.
- See how moving-grid and finite-difference ideas work together to handle complex wave interactions without sacrificing convergence.
- Explore scalar and system cases, including how CFL conditions affect stability and accuracy.

Ideal for readers of numerical analysis, computational fluid dynamics, and applied mathematics who want a solid, accessible treatment of modern schemes for hyperbolic problems.

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