In this paper we generalise results regarding the order of accuracy of finite difference operators on Summation-By-Parts (SBP) form, previously known to hold on uniform grids, to grids with arbitrary point distributions near domain boundaries. We give a definite proof that the order of accuracy in the interior of a diagonal norm based SBP operator must be at least twice that of the boundary ste...

The first and second order of accuracy stable difference schemes for the numerical solution of the mixed problem for the fractional parabolic equation are presented. Stability and almost coercive stability estimates for the solution of these difference schemes are obtained. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of one-dimension...

In this note we consider the application of the WENO scheme to simulations of steady-state flow in a converging diverging nozzle. We demonstrate the recovery of design accuracy through Gegenbauer postprocessing, despite the degradation of the order of accuracy for the numerical solution of the Euler equations to first-order in regions where the characteristics passed through the shock. We have ...

Biodiesel is a promising non-toxic and biodegradable alternative fuel in transport sector. Of all the biodiesel properties, specific gravity and viscosity are the most significant for the effects they have on the utilization of biodiesel fuels in unmodified engines. This paper presents models, which have been derived from experimental data, for predicting the specific gravity and dynamic viscos...

The Cauchy problem for a semilinear parabolic equation is considered. Under the conditions u(x, t) = X(x)T1(t) + T2(t), ∂u ∂x = 0, it is shown that the problem is equivalent to the system of two ordinary differential equations for which exact difference scheme (EDS) with special Steklov averaging and difference schemes with arbitrary order of accuracy (ADS) are constructed on the moving mesh. T...

In this paper, a speed-up strategy for finite volume WENO schemes is developed for solving hyperbolic conservation laws. It adopts p-adaptive like reconstruction, which automatically adjusts from fifth order WENO reconstruction to first order constant reconstruction when nearly constant solutions are detected by the undivided differences. The corresponding order of accuracy for the solutions is...

The parametric cubic curve is a well-developed subject in the field of computer-aided design. Yet there are still some aspects of its nature that need to be more fully investigated. In this paper, formulations of composite PC curves are presented in an order of increasing rigorousness and order of accuracy. A unique PC curve formulation is developed for the practical use in circle approximation...

In standard equispaced finite difference (FD) formulas, symmetries can make the order of accuracy relatively high compared to the number of nodes in the FD stencil. With scattered nodes, such symmetries are no longer available. The generalization of compact FD formulas that we propose for scattered nodes and radial basis functions (RBFs) achieves the goal of still keeping the number of stencil ...

A unified approach to approximating spatial derivatives in particle methods using integral operators is presented. The approach is an extension of particle strength exchange, originally developed for treating the Laplacian in advection–diffusion problems. Kernels of high order of accuracy are constructed that can be used to approximate derivatives of any degree. A new treatment for computing de...