In many problems, one wishes to solve the Helmholtz equation in cylindrical or spherical coordinates which introduces variable coefficients within the differentiated terms. Fourth order accurate methods are desirable to reduce pollution and dispersion errors and so alleviate the points-per-wavelength constraint. However, the variable coefficients renders existing fourth order finite difference ...

‎In this paper‎, ‎the fractional--order form of three dimensional chemostat model with variable yields is introduced‎. ‎The stability analysis of this fractional system is discussed in detail‎. ‎In order to study the dynamic behaviours of the mentioned fractional system‎, ‎the well known nonstandard (NSFD) scheme is implemented‎. ‎The proposed NSFD scheme is compared with the forward Euler and ...

We prove the convergence of line iterative methods for solving the linear system arising from a 9-point compact discretization of a special two dimensional convection-diiusion equation. The results provide rigorous justiication for the numerical experiments conducted elsewhere, which demonstrate the high accuracy and stability advantages of the fourth-order compact scheme.

Fuqiang Lu, Zhiyao Song and Zhuo Zhang Key Laboratory of Virtual Geographic Environment (Nanjing Normal University), Ministry of Education, Nanjing, 210023, China State Key Laboratory Cultivation Base of Geographical Environment Evolution (Jiangsu Province), Nanjing, 210023, China Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanji...

In this paper we review fourth-order approximations of the biharmonic operator in one, two and three dimensions. In addition, we describe recent developments on second and fourth order finite difference approximations of the two dimensional Navier-Stokes equations. The schemes are compact both for the biharmonic and the Laplacian operators. For the convective term the fourth order scheme invoke...