This book deals with numerical methods for solving partial differential equa tions (PDEs)
coupling advection, diffusion and reaction terms, with a focus on time-dependency. A …

Time-dependent advection–diffusion–reaction and diffusion–reaction equations are used as
models in biology, chemistry, physics, and engineering. As representative examples, we …

This paper deals with the numerical solution of the Heston partial differential equation (PDE)
that plays an important role in financial option pricing theory, Heston (1993). A feature of this …

In this paper, we introduce a new numerical scheme, based on the ADI (alternating direction
implicit) method, to price American put options with a stochastic volatility model. Upon …

This report analyzes the long time stability of four methods for non-iterative, sub-physics,
uncoupling for the evolutionary Stokes–Darcy problem. The four methods uncouple each …

In this paper, a meshless finite difference (FD) method with B-splines is presented for
numerical solution of coupled advection-diffusion-reaction (ADR) problems. The proposed …

We consider Alternating Direction Implicit (ADI) schemes for the numerical solution of initial-
boundary value problems for convection–diffusion equations with cross derivative terms. We …

We consider the unconditional stability of second-order ADI schemes in the numerical
solution of finite difference discretizations of multi-dimensional diffusion problems containing …

Ocean models usually rely on a tracer mixing operator which diffuses along isoneutral
directions. This requirement is imposed by the highly adiabatic nature of the oceanic interior …

In this paper we consider the numerical solution of 2D systems of certain types of taxis-
diffusion-reaction equations from mathematical biology. By spatial discretization these PDE …