We prove that the first-order theory of the Medvedev degrees, the first-order theory of the Muchnik degrees, and the third-order theory of true arithmetic are pairwise recursively isomorphic (obtained independently by Lewis, Nies, and Sorbi [7]). We then restrict our attention to the degrees of closed sets and prove that the following theories are pairwise recursively isomorphic: the first-orde...

A third-order compact gas-kinetic scheme is proposed for three-dimensional compressible flow computations. The new based on three key ingredients: the time-accurate gas evolution model interface flux, Hermite weighted essentially nonoscillatory reconstruction, and two-stage temporal discretization. In contrast to Riemann-solver-based methods, due use of flux function can achieve a accuracy with...

We present a new higher-order accurate finite difference explicit jump Immersed Interface Method for solving two-dimensional elliptic problems with singular source and discontinuous coefficients in the irregular region on compact Cartesian mesh. propose strategy discretizing solution at points nine-point stencil such that compactness is maintained throughout whole computational domain. The sche...