Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.

Common And Endangered Species: How Does Society Allocate Support For Their Conservation

Examines how society allocates support for species’ conservation when numbers involved are large and resources are limited. Rational behaviour suggests that species in urgent need of conservation will receive more support than those species that are common. However, we demonstrate that in the absence of balanced knowledge common species will receive support more than they would otherwise receive despite society placing high existence values on all species. Twenty four species, both common and endangered and some with a restricted distribution, are examined. We demonstrate that balanced information is vital in order to direct more support for species that are endangered than those that are not. Implications for conservation stemming from the findings are discussed.