Article history: Received 10 June 2010 Received in revised form 22 February 2011 Accepted 24 February 2011 Available online 1 March 2011

4 FDM's for u ′ = f (t, u) 105 4.1 Convergence and stability of explicit, one step FDM's for u ′ =

In this paper a space-time fractional wave equation on a finite domain is considered. The time and space fractional derivative are described in the Caputo sense. We propose a finite difference scheme to solve the space-time fractional wave equation. We discuss about stability and convergence of the method and prove that the finite difference scheme is unconditionally stable and convergent with ...

Article history: Received 24 March 2015 Received in revised form 25 September 2015 Accepted 1 November 2015 Available online 4 November 2015

We describe and discuss the properties of three numerical methods for solving the diffusion equation for the transport of the chemical species and of the angular momentum in stellar interiors. We study through numerical experiments both their accuracy and their ability to provide physical solutions. On the basis of new tests and analyses applied to the stellar astrophysical context, we show tha...

Lubrication equations are fourth order degenerate diffusion equations of the form ht + ∇ · (f(h)∇∆h) = 0, describing thin films or liquid layers driven by surface tension. Recent studies of singularities in which h → 0 at a point, describing rupture of the fluid layer, show that such equations exhibit complex dynamics which can be difficult to simulate accurately. In particular, one must ensure...

Starting from a high-order local nonreflecting boundary condition (NBC) for single scattering [25], we derive a local NBC for time-dependent multiple scattering problems, which is completely local both in space and time. To do so, we first develop an exterior evaluation formula for a purely outgoing wave field, given its values and those of certain auxiliary functions needed for the local NBC a...

Contents Preface Introduction xv 1 1.1 A one-dimensional model problem 2 1.2 A two-dimensional example of heat propagation in a heterogeneous material 3 1.3 Examples of irregular domains and free boundary problems 5 1.4 The scope of the monograph and the methodology 5 1.4.1 Jump conditions 7 1.4.2 The choice of grids 7 1.5 A minireview of some popular finite difference methods for interface pro...