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Open Access Research Article

A mathematical model of water pollution measurement in a stream using a collocation method with a higher order Legendre polynomial

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pp. 1973–1980Vol. 28Issue 5August 2025DOI: 10.47974/JIM-2184XML
Received:
09 Aug 2024
Published Online:
19 Aug 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2184
Pages:
1973–1980

Abstract

In environmental research, challenges with water contamination assessment are generally prevalent. Through data collection, pollution levels in a system may be determined. This is quite challenging and involved; the measurements of what was measured vary from one point to another in every location. The governing equations for a uniform flow pollution dispersion model are used in water quality modeling. The advection-diffusion-reaction equation used in water quality model-ing for a uniform flow stream is a stable pollution dispersion model. This study presents a one-dimensional mathematical model for measuring stream water quality by collocation higher order Legendre polynomial functions. A water pol-lutant concentration can be approximated using the collocation method. A related water quality quantification method may also be employed with the suggested mathematical simulation to approximate the solution. 

Keywords

Subject Classifications

65N06

References

[1] N. Pochai, S. Tangmanee, L. J. Crane, and J. J. H. Miller, “A mathematical model of water pollution control using the finite element method,” Proc. Appl. Math. Mech. (PAMM), vol. 6, no. 1, pp. 755–756 (2006).
[2] N. Pochai, S. Tangmanee, L. J. Crane, and J. J. H. Miller, “A water quality computation in the uniform channel,” J. Interdiscip. Math., vol. 11, no. 6, pp. 803–814 (2008).
[3] N. Pochai, “A numerical computation of non-dimensional form of stream water quality model with hydrodynamic advection-dispersion-reaction equations,” J. Nonlinear Anal.: Hybrid Syst., vol. 3, pp. 666–673 (2009).
[4] N. Pochai and R. Depana, “A numerical computation of water quality measurement in a uniform channel using a finite difference method,” Procedia Eng., vol. 8, pp. 85–88 (2011).
[5] N. Pochai, “A numerical treatment of non-dimensional form of water quality model in a non-uniform flow stream using Saulyev scheme,” Math. Probl. Eng., vol. 2011, Art. ID 491317 (2011).
[6] N. Pochai and R. Depana, “An optimal control of water pollution in a stream using a finite difference method,” World Acad. Sci. Eng. Technol., vol. 6, no. 56, pp. 1186–1188 (2011).
[7] N. Pochai, “A numerical computation of non-dimensional form of a nonlinear hydrodynamic model in a uniform reservoir,” J. Nonlinear Anal.: Hybrid Syst., vol. 3, pp. 463–466 (2009).
[8] N. Pochai, S. Tangmanee, L. J. Crane, and J. J. H. Miller, “A water quality computation in the uniform reservoir,” J. Interdiscip. Math., vol. 12, no. 1, pp. 19–28 (2009).
[9] N. Pochai, S. Tangmanee, L. J. Crane, and J. J. H. Miller, “A finite element simulation of water quality measurement in the open reservoir,” Thai J. Math., vol. 7, no. 2, pp. 77–93 (2009).
[10] N. Pochai and J. Sornsri, “A non-dimensional form of hydrodynamic model with variable coefficients in a uniform reservoir using Lax-Wendroff method,” Procedia Eng., vol. 8, pp. 89–93 (2011).
[11] F. Mabood and N. Pochai, “Asymptotic solution for a water quality model in a uniform stream,” Int. J. Eng. Math., vol. 2013, Art. ID 135140, 4 pp (2013).
[12] N. Pochai, “Numerical treatment of a modified MacCormack scheme in a nondimensional form of the water quality models in a nonuniform flow stream,” J. Appl. Math., vol. 2014, Art. ID 274263, 8 pp (2014).
[13] W. Klaychang and N. Pochai, “A numerical treatment of a non-dimensional form of a water quality model in the Rama-nine reservoir,” J. Interdiscip. Math., vol. 18, no. 4, pp. 375–394 (2015).
[14] B. Bradie, A Friendly Introduction to Numerical Analysis. Upper Saddle River, NJ, USA: Pearson Prentice Hall (2006).
[15] G. E. Fasshauer, Numerical Methods for Differential Equations Handouts. Chicago, IL, USA (2007).
[16] G. E. Fasshauer, Meshfree Approximation Methods with MATLAB, Interdisciplinary Mathematical Sciences – Vol. 6. Singapore: World Scientific Publishers (2007).
[17] T. D. Rao and S. Chakraverty, “Solving uncertain differential equations using interval Legendre polynomials based collocation method,” J. Interdiscip. Math., vol. 22, no. 4, pp. 473–491 (2019).

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