Anziam Journal 

About: Anziam Journal is an academic journal published by Cambridge University Press. The journal publishes majorly in the area(s): Boundary value problem & Nonlinear system. It has an ISSN identifier of 1446-1811. Over the lifetime, 1688 publications have been published receiving 12097 citations. The journal is also known as: Australian & New Zealand industrial and applied mathematics journal & Australian and New Zealand industrial and applied mathematics journal.

A generalization of the Bernstein polynomials based on the q -integers

Abstract: This paper is concerned with a generalization of the Bernstein polynomials in which the approximated function is evaluated at points spaced in geometric progression instead of the equal spacing of the original polynomials.

Regularity of solutions to a time-fractional diffusion equation

Abstract: We prove estimates for the partial derivatives of the solution to a time-fractional diffusion equation posed over a bounded spatial domain. Such estimates are needed for the analysis of effective numerical methods, particularly since the solution is typically less regular than in the familiar case of classical diffusion. doi:10.1017/S1446181111000617

Adaptive sparse grids

Abstract: Sparse grids, as studied by Zenger and Griebel in the last 10 years have been very successful in the solution of partial differential equations, integral equations and classification problems. Adaptive sparse grid functions are elements of a function space lattice. Such lattices allow the generalisation of sparse grid techniques to the fitting of very high-dimensional functions with categorical and continuous variables. We have observed in first tests that these general adaptive sparse grids allow the identification of the ANOVA structure and thus provide comprehensible models. This is very important for data mining applications. Perhaps the main advantage of these models is that they do not include any spurious interaction terms and thus can deal with very high dimensional data.

The time fractional diffusion equation and the advection-dispersion equation

Abstract: The time fractional diffusion equation with appropriate initial and boundary conditions in an n-dimensional whole-space and half-space is considered. Its solution has been obtained in terms of Green functions by Schneider and Wyss. For the problem in whole-space, an explicit representation of the Green functions can also be obtained. However, an explicit representation of the Green functions for the problem in half-space is difficult to determine, except in the special cases D 1 with arbitrary n ,o rn D 1 with arbitrary .I n this paper, we solve these problems. By investigating the explicit relationship between the Green functions of the problem with initial conditions in whole-space and that of the same problem with initial and boundary conditions in half-space, an explicit expression for the Green functions corresponding to the latter can be derived in terms of Fox functions. We also extend some results of Liu, Anh, Turner and Zhuang concerning the advection-dispersion equation and obtain its solution in half-space and in a bounded space domain.

A chebyshev pseudo-spectral method for solving fractional-order integro-differential equations

Abstract: A Chebyshev pseudo-spectral method for solving numerically linear and nonlinear fractional-order integro-differential equations of Volterra type is considered. The fractional derivative is described in the Caputo sense. The suggested method reduces these types of equations to the solution of linear or nonlinear algebraic equations. Special attention is given to study the convergence of the proposed method. Finally, some numerical examples are provided to show that this method is computationally efficient, and a comparison is made with existing results. doi:10.1017/S1446181110000830