SIAM Journal on Numerical Analysis, Vol. 51, No. 4 (2013), pp. 2470-2490 (21 pages) The primary aim of this paper is to answer the question, What are the highest-order five-or nine-point compact ...

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 ...

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

Mathematical approaches for numerically solving partial differential equations. The focus will be (a) iterative solution methods for linear and non-linear equations, (b) spatial discretization and ...

Numerical methods for the primitive equations (PEs) of oceanic flow are presented in this paper. First, a two-dimensional Poisson equation with a suitable boundary condition is derived to solve the ...