Nonlinearly stable compact schemes for shock calculations
SIAM Journal on Numerical Analysis
A three-point combined compact difference scheme
Journal of Computational Physics
A family of high order finite difference schemes with good spectral resolution
Journal of Computational Physics
A three-point sixth-order nonuniform combined compact difference scheme
Journal of Computational Physics
Compact implicit MacCormack-type schemes with high accuracy
Journal of Computational Physics
Implicit, high-resolution, compact schemes for gas dynamics and aeroacoustics
Journal of Computational Physics
A Fourth Order Hermitian Box-Scheme with Fast Solver for the Poisson Problem in a Square
Journal of Scientific Computing
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In this work the authors extend the high order compact difference schemes to the matching technique to develop a Local Matched Reconstruction theory that can be also considered as a generalization of the spline theory. The problem of the high order reconstructions correlated to an optimal matching in overlapping regions for contiguous expansions in one or more dimensions is stressed; some new generalized matched interpolations and their related numerical schemes are presented together with Fourier analysis of errors. Finally, some relevant aspects of the computational efforts associated to the various approaches are discussed.