TL;DR: In this article, the authors present finite-difference schemes for the evaluation of first-order, second-order and higher-order derivatives yield improved representation of a range of scales and may be used on nonuniform meshes.
TL;DR: A new version of ENO (essentially non-oscillatory) shock-capturing schemes which is called weighted ENO, where, instead of choosing the "smoothest" stencil to pick one interpolating polynomial for the ENO reconstruction, a convex combination of all candidates is used.
TL;DR: An hierarchy of uniformly high-order accurate schemes is presented which generalizes Godunov's scheme and its second- order accurate MUSCL extension to an arbitrary order of accuracy.
TL;DR: In this paper, the Runge?Kutta discontinuous Galerkin method for numerically solving hyperbolic conservation laws is extended to multidimensional nonlinear systems of conservation laws.
TL;DR: In this article, the spectral volume (SV) method was proposed to achieve high-order accuracy in an efficient manner similar to spectral element and multidomain spectral methods.