A procedure to switch the order of accuracy of finite difference schemes is developed. The development is based on existing Summation-By-Parts operators and a weak interface treatment. The resulting scheme is proven to be stable and accurate. Numerical experiments verify the theoretical accuracy for smooth solutions. In addition shock calculations is performed, using a scheme where the develope...

L∞ SOLUTIONS FOR A MODEL OF NONISOTHERMAL POLYTROPIC GAS FLOW∗ HERMANO FRID† , HELGE HOLDEN‡ , AND KENNETH H. KARLSEN‡ Abstract. We establish the global existence of L∞ solutions for a model of polytropic gas flow with varying temperature governed by a Fourier equation in the Lagrangian coordinates. The result is obtained by showing the convergence of a class of finite difference schemes, which...

A generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations. We prove that for si...

A class of new explicit second order accurate finite difference schemes for the computation of weak solutions of hyperbolic conservation laws is presented. These highly nonlinear schemes are obtained by applying a nonoscillatory first order accurate scheme to an appropriately modified flux function. The so-derived second order accurate schemes achieve high resolution while preserving the robust...