In the present article, the advection–diffusion equation (ADE) having a nonlinear type source/sink term with initial and boundary conditions is solved using finite difference method (FDM). The solution of solute concentration is calculated numerically and also presented graphically for conservative and nonconservative cases. The emphasis is given for the stability analysis, which is an important aspect of the proposed mathematical model. The accuracy and efficiency of the proposed method are validated by comparing the results obtained with existing analytical solutions for a conservative system. The novelty of the article is to show the damping nature of the solution profile due to the presence of the nonlinear reaction term for different particular cases in less computational time by using the reliable and efficient finite difference method.
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April 2019
Research-Article
Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation
Anup Singh,
Anup Singh
Department of Mathematical Sciences,
Indian Institute of Technology (BHU),
Varanasi 221005, India
Indian Institute of Technology (BHU),
Varanasi 221005, India
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S. Das,
S. Das
Department of Mathematical Sciences,
Indian Institute of Technology (BHU),
Varanasi 221005, India
e-mail: sdas.apm@iitbhu.ac.in
Indian Institute of Technology (BHU),
Varanasi 221005, India
e-mail: sdas.apm@iitbhu.ac.in
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S. H. Ong,
S. H. Ong
Institute of Mathematical Sciences,
University of Malaya,
Kuala Lumpur 50603, Malaysia;
University of Malaya,
Kuala Lumpur 50603, Malaysia;
Department of Actuarial Science
and Applied Statistics,
UCSI University,
Kuala Lumpur 56000, Malaysia
and Applied Statistics,
UCSI University,
Kuala Lumpur 56000, Malaysia
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H. Jafari
H. Jafari
Department of Mathematical Sciences,
University of South Africa (UNISA),
Pretoria 0003, South Africa
University of South Africa (UNISA),
Pretoria 0003, South Africa
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Anup Singh
Department of Mathematical Sciences,
Indian Institute of Technology (BHU),
Varanasi 221005, India
Indian Institute of Technology (BHU),
Varanasi 221005, India
S. Das
Department of Mathematical Sciences,
Indian Institute of Technology (BHU),
Varanasi 221005, India
e-mail: sdas.apm@iitbhu.ac.in
Indian Institute of Technology (BHU),
Varanasi 221005, India
e-mail: sdas.apm@iitbhu.ac.in
S. H. Ong
Institute of Mathematical Sciences,
University of Malaya,
Kuala Lumpur 50603, Malaysia;
University of Malaya,
Kuala Lumpur 50603, Malaysia;
Department of Actuarial Science
and Applied Statistics,
UCSI University,
Kuala Lumpur 56000, Malaysia
and Applied Statistics,
UCSI University,
Kuala Lumpur 56000, Malaysia
H. Jafari
Department of Mathematical Sciences,
University of South Africa (UNISA),
Pretoria 0003, South Africa
University of South Africa (UNISA),
Pretoria 0003, South Africa
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 17, 2018; final manuscript received January 16, 2019; published online February 15, 2019. Assoc. Editor: Dumitru Baleanu.
J. Comput. Nonlinear Dynam. Apr 2019, 14(4): 041003 (6 pages)
Published Online: February 15, 2019
Article history
Received:
April 17, 2018
Revised:
January 16, 2019
Citation
Singh, A., Das, S., Ong, S. H., and Jafari, H. (February 15, 2019). "Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation." ASME. J. Comput. Nonlinear Dynam. April 2019; 14(4): 041003. https://doi.org/10.1115/1.4042687
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