We develop a fast and accurate approximation of the normally stiff equations which minimize the Landau–de Gennes free energy of a nematic liquid crystal. The resulting equations are suitable for all configurations in which defects are not present, making them ideal for device simulation. Specifically they offer an increase in computational efficiency by a factor of 100 while maintaining an erro...

Phylogenetic tree reconstruction is a fundamental biological problem. Quartet amalgamation combining a set of trees over four taxa into a tree over the full set stands at the heart of many phylogenetic reconstruction methods. This task has attracted many theoretical as well as practical works. However, even reconstruction from a consistent set of quartet trees, i.e. all quartets agree with some...

in this paper, we propose a new method for solving the stochastic advection-diffusion equation of ito type. in this work, we use a compact finite difference approximation for discretizing spatial derivatives of the mentioned equation and semi-implicit milstein scheme for the resulting linear stochastic system of differential equation. the main purpose of this paper is the stability investigatio...

in this paper, a numerical efficient method is proposed for the solution of time fractionalmobile/immobile equation. the fractional derivative of equation is described in the caputosense. the proposed method is based on a finite difference scheme in time and legendrespectral method in space. in this approach the time fractional derivative of mentioned equationis approximated by a scheme of order o...

The unprecedented rate at which data is being generated has led to the growth of markets where valuable datasets are bought and sold. A salient feature this market that a data-buyer (agent) endowed with multi-dimensional private information, namely her ``ideal'' record she values most how valuation for given changes as its distance from ideal changes. Consequently, revenue-maximization problem ...

In this article, we apply the Multiquadric radial basis function (RBF) interpo-lation method for nding the numerical approximation of traveling wave solu-tions of the Kawahara equation. The scheme is based on the Crank-Nicolsonformulation for space derivative. The performance of the method is shown innumerical examples.

Solving dynamical problems in general relativity requires the full machinery of numerical relativity. Wilson has proposed a simpler but approximate scheme for systems near equilibrium, like binary neutron stars. We test the scheme on isolated, rapidly rotating, relativistic stars. Since these objects are in equilibrium, it is crucial that the approximation work well if we are to believe its pre...