Performance of some finite difference methods for a 3D advection–diffusion equation

A. R. Appadu, J. K. Djoko, H. H. Gidey

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


In this work, a new finite difference scheme is presented to discretize a 3D advection–diffusion equation following the work of Dehghan (Math Probl Eng 1:61–74, 2005, Kybernetes 36(5/6):791–805, 2007). We then use this scheme and two existing schemes namely Crank–Nicolson and Implicit Chapeau function to solve a 3D advection–diffusion equation with given initial and boundary conditions. We compare the performance of the methods by computing l2-error, l-error and some performance indices such as mass distribution ratio, mass conservation ratio, total mass and coefficient of determination (Kvalseth in Am Stat 39(4):279–285, 1985). We then use optimization techniques to improve the results from the numerical methods.

Original languageEnglish
Pages (from-to)1179-1210
Number of pages32
JournalRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Issue number4
Publication statusPublished - Oct 1 2018

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology
  • Computational Mathematics
  • Applied Mathematics


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