A homogeneous linear difference equation with constant coefficients over a locally compact abelian group $G$ is an equation of the form $\sum^n_{j=1} c_jf (t_jx) = 0 ...

This paper describes a new symmetry-based approach to solving a given ordinary difference equation. By studying the local structure of the set of solutions, we derive a systematic method for ...

Ordinary differential equations (ODEs) and difference equations serve as complementary tools in the mathematical modelling of processes evolving in continuous and discrete time respectively. Together ...

In this paper we investigate the effectiveness of alternating direction implicit (ADI) time-discretization schemes in the numerical solution of the three-dimensional Heston-Hull-White partial ...

This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of ...