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首页> 外文期刊>Journal of Computational Physics >Numerical solution of certain classes of transport equations in any dimension by Shannon sampling
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Numerical solution of certain classes of transport equations in any dimension by Shannon sampling

机译：通过Shannon采样求解任意维上某些输运方程的数值解。

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摘要

A method is developed for computing solutions to some class of linear and nonlinear transport equations (hyperbolic partial differential equations with smooth solutions), in any dimension, which exploits Shannon sampling, widely used in information theory and signal processing. The method can be considered a spectral or a wavelet method, strictly related to the existence of characteristics, but allows, in addition, for some precise error estimates in the reconstruction of continuous profiles from discrete data. Non-dissipativity and (in some case) parallelizability are other features of this approach. Monotonicity-preserving cubic splines are used to handle nonuniform sampling. Several numerical examples, in dimension one or two, pertaining to single linear and nonlinear (integro-differential) equations, as well as to certain systems, are given.
机译：开发了一种方法，用于在任何维度上计算一类线性和非线性传输方程（具有光滑解的双曲型偏微分方程）的解，该方法利用了在信息论和信号处理中广泛使用的Shannon采样。该方法可以被认为是频谱方法或小波方法，严格地与特征的存在有关，但此外，它还允许在从离散数据重建连续剖面时进行一些精确的误差估计。非耗散性和（在某些情况下）可并行性是此方法的其他功能。保持单调性的三次样条用于处理非均匀采样。给出了几个一维或一维数值示例，涉及单个线性和非线性（积分微分）方程以及某些系统。

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