Application of differential equations in solving a model of environmental phenomena
Subject Areas : The Application of Chemistry in Environment
1 -
Keywords: environmental science, mathematical modeling, differential equation, ,
Abstract :
Differential equations play a key role in the environmental sciences and provide mathematical tools for understanding environmental processes and predicting changes.
The purpose of the research is to provide mathematical modeling methods to solve environmental problems and to use standard mathematical techniques and methods to solve the model by obtaining the desired results, and the analysis is done based on mathematical laws and ecological system.
In this research, the application of differential equations for environmental modeling, especially in pollutant dispersion, ecosystem dynamics, and climate change prediction, is discussed. In this research, mathematical foundations, modeling method through differential equation is examined and its role in explaining the complexity of the environmental system is revealed.
This paper also points to the potential for future development of differential equations in interdisciplinary topics and more advanced computing, which provides a research context and improvement path for the field of environmental sciences.
[1] Tsokos, C. P., & Xu, Y. (2009). Modeling carbon dioxide emissions with a system of differential equations. Nonlinear Analysis-Theory Methods &
Applications, 71(12), E1182-E1197.
[2] Lu, Z. L., Zhenwei, & Wang, H. L. (2016). The application of regression analysis and differential equation models in the prediction
of indoor PM2.5 concentration. Journal of Residuals Science & Technology, 13(1), 325-328.
[3] Tiwari, J. L., & Hobbie, J. E. (1976). Random differential equations as models of ecosystems .2. Initial condition and parameter
specifications in terms of maximum entropy distributions. Mathematical Biosciences, 31(1-2), 37-53.
[4] Liu, Y. L., Chen, C., Alotaibi, R., & Shorman, S. M. (2022). Study on audio-visual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation. Applied Mathematics and Nonlinear
Sciences, 7(2), 307-314.
[5] Kafle, R. C., Pokhrel, K. P., Khanal, N., & Tsokos, C. P. (2019). Differential equation model of carbon dioxide emission using functional linear regression. Journal of Applied Statistics, 46(7), 1246-1259.
[6] Cai, W. G., & Pan, J. F. (2017). Stochastic differential equation models for the price of European CO2 emissions allowances. Sustainability, 9(2), 207.
[7] Gulliver, J.S. (2007). Introduction to chemical transport in the environment. Cambridge University Press.
[8] Chapra, S.C. (1997). Surface water-quality modeling, Vol. 1, McGraw- Hill New York.
[9] Massabó, M., Cianci, R. and Paladino, O. (2011).An analytical solution of the advection dispersion equation in a bounded domain and its application to laboratory experiments, Journal of Applied Mathematics, V. 2011, Art. ID. 493014, 14p.
[10] Mikhaĭlov, M.D. and Özişik, M.N. (1984). Unified analysis and solutions of heat and mass diffusion,
[11] Pérez Guerrero, J., et al., (2009). Analytical solution of the advection–diffusion transport equation using a change-of-variable and integral
transform technique, International Journal of Heat and Mass Transfer, 52(13), pp. 3297-3304.[12] Van Genuchten, M.T. and Alves, W. (1982). Analytical solutions of the one-dimensional convective-dispersive solute transport equation, Technical Bulletin, 1982(1661).
[13] Barati Moghaddam M, Mazaheri M, MohammadVali Samani J. Numerical Solution of Advection-Dispersion Equation with Temporal Conservation Zones in Case of Unsteady Flow in Irregular Sections. Journal of Science And Irrigation Engineering.2015;40)1(: 99-117.[in Persian]
[14] A. Parsaie, A.H. Haghiabi, Calculation of Longitudinal Dispersion Coefficient and Modeling of Pollution transport in Rivers )Case Study: Severn and Narew Rivers(, Water and Soil, 29 )5( )2015( 1070-1085. [in Persian]