High-order simulation of flows containing shock waves is an extremely difficult task due to the discontinuous changes in flow properties across the shock. The present work investigates a shock-detecting sensor for filtering of high-order compact finitedifference schemes to examine the shock-capturing in direct simulation of NavierStokes solver. Based on the accuracy and minimum dissipation erro...

We discuss a number of numerical methods that approximate the solution of the Partial Integro Differential Equation (PIDE) that models contingent claims with jumps. Starting with the Merton jump model for the underlying asset we motivate how to find the corresponding PIDE that models a derivative quantity on that asset. We pose the PIDE in a form that becomes amenable to a solution using the fi...

Ericksen Leslie equation describes the time evolution of a spin vector and velocity in liquid crystals. This equation has following property: (i) the length preserving of a spin vector, (ii) the energy conservation or the dissipation property, (iii) the incompressibility of a velocity vector. In physics papers, the fourth order Runge-Kutta’s method is used for numerical analysis of some types o...

In this work, the method of radial basis functions is used for finding the solution of an inverse problem with source control parameter. Because a much wider range of physical phenomena are modelled by nonclassical parabolic initial-boundary value problems, theoretical behavior and numerical approximation of these problems have been active areas of research. The radial basis functions (RBF) met...

A model of the lattice Boltzmann method for non-Newtonian fluids was constructed. The shear stress of purely viscous but non-elastic non-Newtonian fluid is a function of shear rate only. For the power-law model, only two constant parameters can cover shear-thinning and shear-thickening fluids. Two power-law models are introduced to the finite difference lattice Boltzmann method. One is a model ...