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

Maxwell's equations form the cornerstone of electromagnetic theory, offering a complete description of how electric and magnetic fields interact with matter. In combination with state‐of‐the‐art ...

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 ...

SIAM Journal on Numerical Analysis contains research articles on the development and analysis of numerical methods including their convergence, stability, and error ...

In this paper, we discuss efficient pricing methods via a partial differential equation (PDE) approach for long-dated foreign exchange (FX) interest rate hybrids under a three-factor multicurrency ...

Introductory course on using a range of finite-difference methods to solve initial-value and initial-boundary-value problems involving partial differential equations. The course covers theoretical ...

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 ...

At a quick glance, could you tell the difference between a group of 20 dots and a group of 30? What about 20 and 21? It seems like there must be a point at which you'd simply be guessing, but recent ...