Simulation of advection–diffusion–dispersion equations based on a composite time discretization scheme

Abstract

In this work, we develop a high-order composite time discretization scheme based on classical collocation and integral deferred correction methods in a backward semi-Lagrangian framework (BSL) to simulate nonlinear advection-diffusion-dispersion problems. The third-order backward differentiation formula and fourth-order finite difference schemes are used in temporal and spatial discretizations, respectively. Additionally, to evaluate function values at non-grid points in BSL, the constrained interpolation profile method is used. Several numerical experiments demonstrate the efficiency of the proposed techniques in terms of accuracy and computation costs, compare with existing departure traceback schemes.

Error estimation using neural network technique for solving ordinary differential equations

“…For this reason, several numerical techniques for solving ODEs have been developed during last few decades. Also, the numerical methods can be broadly classified into the following categories: the first class consists of one-step multistage techniques such as Runge-Kutta-type methods [5,13,17], the second includes BDF-type multistep methods [6], and the last is a group of deferred or error correction methods [4,7,18,19] such as spectral deferred correction (SDC) methods [8,11], etc.…”