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.
Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation
Indian Institute of Technology (BHU),
Varanasi 221005, India
University of Malaya,
Kuala Lumpur 50603, Malaysia;
and Applied Statistics,
Kuala Lumpur 56000, Malaysia
University of South Africa (UNISA),
Pretoria 0003, South Africa
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.
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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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