Numerical solution of the 1D advection-diffusion equation using standard and nonstandard finite difference schemes

DOI10.1155/2013/734374zbMath1266.65140OpenAlexW2165304903WikidataQ59004145 ScholiaQ59004145MaRDI QIDQ2375652

A. R. Appadu

Publication date: 14 June 2013

Published in: Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/734374

Mathematics Subject Classification ID

Diffusion (76R50) Finite difference methods applied to problems in fluid mechanics (76M20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)

Related Items

A meshless technique based on the moving least squares shape functions for nonlinear fractal-fractional advection-diffusion equation ⋮ Implementation of streamline simulation based on finite element method in FEniCS ⋮ A fictitious-play finite-difference method for linearly solvable mean field games ⋮ Numerical Method Combinations Assessment for Transport-Dominated Problems in the CHIMERE Model: A Case Study of Agadir (Morocco) ⋮ Time-splitting procedures for the numerical solution of the 2D advection-diffusion equation ⋮ A computational study of three numerical methods for some advection-diffusion problems ⋮ A time-spectral method for initial-value problems using a novel spatial subdomain scheme ⋮ Performance of some finite difference methods for a 3D advection-diffusion equation ⋮ An efficient Mickens' type NSFD scheme for the generalized Burgers Huxley equation ⋮ Exact and nonstandard finite difference schemes for the generalized KdV-Burgers equation ⋮ On the performance of some NSFD methods for a 2-D generalized Burgers–Huxley equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dispersion-relation-preserving finite differene schemes for computational acoustics
• The controversial stability analysis
• Weighted finite difference techniques for the one-dimensional advection-diffusion equation.
• A family of low dispersive and low dissipative explicit schemes for flow and noise computations.
• A method for reducing dispersion in convective difference schemes
• Heat transfer to a draining film
• On the numerical solution of the one-dimensional convection-diffusion equation
• Optimal and near–optimal advection–diffusion finite–difference schemes. V. Error propagation
• Some applications of the concept of minimized integrated exponential error for low dispersion and low dissipation
• The concept of minimized integrated exponential error for low dispersion and low dissipation schemes
• The stability of explicit Euler time-integration for certain finite difference approximations of the multi-dimensional advection-diffusion equation
• Numerical solutions for solute transport in unconfined aquifers