Numerical Solution of Two-Dimensional Advection–Diffusion Equation Using Generalized Integral Representation Method

Abstract

Generalized integral representation method (GIRM) is designed to numerically solve initial and boundary value problems for differential equations. In this work, we develop numerical schemes based on 1- and 2-step GIRMs for evaluation of the two-dimensional problem of advective diffusion in an infinite domain. Accurate approximate solutions are obtained in both cases of GIRM and compared to the exact ones. The derivation of GIRM is straightforward and implementation is simple.

Propagator integral method for plasma physics kinetic equations with practical applications

“…Under this perspective, integral methods [22,29,[31][32][33][37][38][39][40] provide a robust semianalytical scheme to obtain a suitable time evolving solution for a great variety of problems. The lack of discretisation that characterises these schemes allows to obtain consistent transient and steady solutions even if abrupt or sharp parameters, initial or boundary conditions appear.…”

“…Unlike in the 1D1V case, here the diffusive matrix is usually non-singular. The general equation that describes these problems can be obtained by setting N = 2 in (2.10) becoming 38) where q i is the velocity component in the i-direction and D i and D ij their associated drift-diffusion coefficients.…”