Hyperbolic partial differential equations describe wave behavior.

Hyperbolic partial differential equations describe time-dependent wave behavior. Examples of applications modeled by hyperbolic PDEs include:

  • Fluid dynamics
  • Water waves
  • Acoustic waves
  • Electromagnetic waves

Nonlinear hyperbolic PDEs pose a unique computational challenge because of the tendency of discontinuities (shocks) to appear even in solutions with smooth initial data. Numerical methods deal with these discontinuities by using limiters (to avoid oscillation in the computation of derivatives) and Riemann solvers (local solutions based on piecewise constant discontinuous data).

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