Sinc methods for quadrature and differential equations
Sinc methods for quadrature and differential equations
Monotonicity-preserving interpolation of nongridded data
Computer Aided Geometric Design
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
Orthogonal Sampling Formulas: A Unified Approach
SIAM Review
Monotonic Cubic Spline Interpolation
CGI '99 Proceedings of the International Conference on Computer Graphics
Comonotone parametric C1 interpolation of nongridded data
Journal of Computational and Applied Mathematics
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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.