The finite difference time domain (FDTD) method is commonly used as a numerically accurate way of propagating sound. However, it requires extensive computation. We present a simple method for accelerating FDTD. Specifically, we modify the FDTD update loop to prioritize computation where it is needed most in order to faithfully propagate waves through the simulated space. We estimate for each po...

The time of nonlinear wave collapse is computed numerically for the Hopf equation. Previous numerical criteria for locating the time of wave collapse are either computationally prohibitive to implement or give erroneous results. A new criterion for this purpose is developed analytically using asymptotic analysis of the wave shock development shortly after breaking. The criterion defines the wav...

Although CLP(R) is a promising application of the logic programming paradigm to numerical computation, it has not addressed what has long been known as \the pitfalls of numerical] computation" 12]. These show that rounding errors induce a severe correctness problem wherever oating-point computation is used. Independently of logic programming, constraint processing has been applied to problems i...