Numerical solution of certain classes of transport equations in any dimension by Shannon sampling

DOI10.1016/j.jcp.2010.01.013zbMath1187.65142OpenAlexW2053454891MaRDI QIDQ964274

Silvia Palpacelli, Romina Gobbi, Renato Spigler

Publication date: 15 April 2010

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2010.01.013

zbMATH Keywords

error estimatesnumerical examplescubic splinesspectral methodinformation theorysignal processingcharacteristicsShannon samplingnonlinear transport equationsShannon waveletsintegro-differential hyperbolic equations

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) Other nonlinear integral equations (45G10) First-order nonlinear hyperbolic equations (35L60) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Numerical methods for wavelets (65T60) Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs (65M25) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Sampling theory in information and communication theory (94A20)

Related Items (1)

A backward approach to certain class of transport equations in any dimension based on the Shannon sampling theorem

Cites Work

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• A Mathematical Theory of Communication
• The fast sinc transform and image reconstruction from nonuniform samples in \(k\)-space
• Approximations via Whittaker's cardinal function
• Monotonicity-preserving interpolation of nongridded data
• Approximating a bandlimited function using very coarsely quantized data: a family of stable sigma-delta modulators of arbitrary order
• An energy-minimization framework for monotonic cubic spline interpolation
• Crystal precipitation with discrete initial data
• Comonotone parametric \(C^ 1\) interpolation of nongridded data
• NUMERICAL TREATMENT OF A NONLINEAR NONLOCAL TRANSPORT EQUATION MODELING CRYSTAL PRECIPITATION
• The Shannon sampling theorem—Its various extensions and applications: A tutorial review
• Numerical Methods Based on Whittaker Cardinal, or Sinc Functions
• Sampling Theory for not Necessarily Band-Limited Functions: A Historical Overview
• A "Sinc-Galerkin" Method of Solution of Boundary Value Problems
• Total variation diminishing Runge-Kutta schemes
• Orthogonal Sampling Formulas: A Unified Approach
• Whittaker's Cardinal Function in Retrospect

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