TY - JOUR
T1 - Performance of some finite difference methods for a 3D advection–diffusion equation
AU - Appadu, A. R.
AU - Djoko, J. K.
AU - Gidey, H. H.
N1 - Funding Information:
Dr Appadu is grateful to the South African DST/NRF SARChI Chair on Mathematical Models and Methods in Bioengineering and Biosciences of the University of Pretoria and to the National Research Foundation of South African Grant Number 95864. Prof. J.K. Djoko is funded through the incentive fund N00 401 Project 85796. Dr Hagos is grateful to DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) for the financial support for 2016. The authors are grateful to the reviewers for their comments which were useful in clarifying and focusing the presentation.
Funding Information:
Acknowledgements Dr Appadu is grateful to the South African DST/NRF SARChI Chair on Mathematical Models and Methods in Bioengineering and Biosciences of the University of Pretoria and to the National Research Foundation of South African Grant Number 95864. Prof. J.K. Djoko is funded through the incentive fund N00 401 Project 85796. Dr Hagos is grateful to DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) for the financial support for 2016. The authors are grateful to the reviewers for their comments which were useful in clarifying and focusing the presentation.
Publisher Copyright:
© 2017, Springer-Verlag Italia S.r.l.
PY - 2018/10/1
Y1 - 2018/10/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s13398-017-0414-7
DO - 10.1007/s13398-017-0414-7
M3 - Article
AN - SCOPUS:85053701098
SN - 1578-7303
VL - 112
SP - 1179
EP - 1210
JO - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
JF - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
IS - 4
ER -