It has long been known that high frequency components, typically from nonsmooth data, can cause spurious oscillations in numerical schemes. Luskin and Rannacher for the Crank-Nicolson scheme, and Rannacher for diagonal Padé schemes in general, discovered that the use of (m − 1, …
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The development of three-dimensional solutions using fluid parabolic equations is an active area of research in underwater acoustics. Several approaches for solving the time-harmonic three-dimensional parabolic equation have been attempted: such as an N × 2D approach developed b…
New algorithms for the matrix exponential and its Fréchet derivative are presented. First, we derive a new scaling and squaring algorithm (denoted expm[new]) for computing eA, where A is any square matrix, that mitigates the overscaling problem. The algorithm is built on the alg…