Research Article
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Year 2021, , 81 - 88, 30.06.2021
https://doi.org/10.47000/tjmcs.879627

Abstract

References

  • [1] Babolian, E., Biazar, J., Vahidi, A.R., A new computational method for Laplace transforms by decomposition method, Applied Mathematics and Computation, 150(2004), 841–846.
  • [2] Biazar, J., Farrokhi, L., Islam, M.R., Modeling the pollution of a system of lakes, Applied Mathematics and Computation, 178(2006), 423–430.
  • [3] Biazar, J., Shahbala, M., Ebrahimi, H., VIM for Solving the Pollution Problemof a Systemof Lakes, Hindawi Publishing Corporation, Journal of Control Science and Engineering, 2010(2010), Article ID 829152, 6 pages, doi:10.1155/2010/829152.
  • [4] Doğan, N., Solution Of The System Of Ordinary Differential Equations By Combined Laplace Transform-Adomian Decomposition Method, Mathematical and Computational Applications An International Journal, 17(2012), 203-211.
  • [5] Doğan, N., Akin, Ö ., Series solution of epidemic model, TWMS Journal of Applied and Engineering Mathematics, 2(2)(2012), 238-244.
  • [6] Doğan, N., Numerical treatment of the model for HIV infection of CD4+T cells by using Multi-Step Laplace Adomian Decomposition Method, Discrete Dynamics in Nature and Society , 2012(2012), Article ID 976352, 11 pages, doi:10.1155/2012/976352.
  • [7] Doğan, N., Numerical solution of Chaotic Genesio System with Multi-Step Laplace Adomian Decomposition Method, Kuwait Journal of Science, 40(2013).
  • [8] Khuri, S.A., A Laplace Decomposition Algorithm Applied To A Class Of Nonlinear Differential Equations, Journal of Applied Mathematics, 1(4)(2001), 141–155.
  • [9] Kiymaz, O., An Algorithm for Solving Initial Value Problems Using Laplace Adomian Decomposition Method, Applied Mathematical Sciences, 3(30)(2009), 1453 – 1459.
  • [10] Merdan, M., He’s Variational Iteration Method Applied To The Solution Of Modelling The Pollution Of A System Of Lakes, Dumlupınar Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 18(Nisan 2009), 59–70.
  • [11] Merdan, M., Homotopy Perturbatıon Method For Solvıng Modellıng The Pollutıon Of A System Of Lakes, SDU Journal Of Science (E-Journal), 4(1)(2009), 99-111.
  • [12] Wazwaz, A., The combined Laplace transform–Adomian decomposition method for handling nonlinear Volterra integro–differential equations, Applied Mathematics and Computation,216(2010), 1304–1309.

Series Solution of Modelling the Pollution

Year 2021, , 81 - 88, 30.06.2021
https://doi.org/10.47000/tjmcs.879627

Abstract

In this article, an approximate analytical series solution of Modeling the
pollution of a lake system is given. Laplace-Adomian decomposition method
(LADM) was used for the serial solution. LADM with different input values has
been used for the solution. The solutions obtained by LADM were compared with
the results obtained by Fourth Order Runge Method. In addition, the results are
compared with residual errors. These comparisons show that LADM is a powerful
method for obtaining approximate solutions to the problem of modeling the
pollution of a lake system.

References

  • [1] Babolian, E., Biazar, J., Vahidi, A.R., A new computational method for Laplace transforms by decomposition method, Applied Mathematics and Computation, 150(2004), 841–846.
  • [2] Biazar, J., Farrokhi, L., Islam, M.R., Modeling the pollution of a system of lakes, Applied Mathematics and Computation, 178(2006), 423–430.
  • [3] Biazar, J., Shahbala, M., Ebrahimi, H., VIM for Solving the Pollution Problemof a Systemof Lakes, Hindawi Publishing Corporation, Journal of Control Science and Engineering, 2010(2010), Article ID 829152, 6 pages, doi:10.1155/2010/829152.
  • [4] Doğan, N., Solution Of The System Of Ordinary Differential Equations By Combined Laplace Transform-Adomian Decomposition Method, Mathematical and Computational Applications An International Journal, 17(2012), 203-211.
  • [5] Doğan, N., Akin, Ö ., Series solution of epidemic model, TWMS Journal of Applied and Engineering Mathematics, 2(2)(2012), 238-244.
  • [6] Doğan, N., Numerical treatment of the model for HIV infection of CD4+T cells by using Multi-Step Laplace Adomian Decomposition Method, Discrete Dynamics in Nature and Society , 2012(2012), Article ID 976352, 11 pages, doi:10.1155/2012/976352.
  • [7] Doğan, N., Numerical solution of Chaotic Genesio System with Multi-Step Laplace Adomian Decomposition Method, Kuwait Journal of Science, 40(2013).
  • [8] Khuri, S.A., A Laplace Decomposition Algorithm Applied To A Class Of Nonlinear Differential Equations, Journal of Applied Mathematics, 1(4)(2001), 141–155.
  • [9] Kiymaz, O., An Algorithm for Solving Initial Value Problems Using Laplace Adomian Decomposition Method, Applied Mathematical Sciences, 3(30)(2009), 1453 – 1459.
  • [10] Merdan, M., He’s Variational Iteration Method Applied To The Solution Of Modelling The Pollution Of A System Of Lakes, Dumlupınar Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 18(Nisan 2009), 59–70.
  • [11] Merdan, M., Homotopy Perturbatıon Method For Solvıng Modellıng The Pollutıon Of A System Of Lakes, SDU Journal Of Science (E-Journal), 4(1)(2009), 99-111.
  • [12] Wazwaz, A., The combined Laplace transform–Adomian decomposition method for handling nonlinear Volterra integro–differential equations, Applied Mathematics and Computation,216(2010), 1304–1309.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Nurettin Doğan 0000-0002-8267-8469

Publication Date June 30, 2021
Published in Issue Year 2021

Cite

APA Doğan, N. (2021). Series Solution of Modelling the Pollution. Turkish Journal of Mathematics and Computer Science, 13(1), 81-88. https://doi.org/10.47000/tjmcs.879627
AMA Doğan N. Series Solution of Modelling the Pollution. TJMCS. June 2021;13(1):81-88. doi:10.47000/tjmcs.879627
Chicago Doğan, Nurettin. “Series Solution of Modelling the Pollution”. Turkish Journal of Mathematics and Computer Science 13, no. 1 (June 2021): 81-88. https://doi.org/10.47000/tjmcs.879627.
EndNote Doğan N (June 1, 2021) Series Solution of Modelling the Pollution. Turkish Journal of Mathematics and Computer Science 13 1 81–88.
IEEE N. Doğan, “Series Solution of Modelling the Pollution”, TJMCS, vol. 13, no. 1, pp. 81–88, 2021, doi: 10.47000/tjmcs.879627.
ISNAD Doğan, Nurettin. “Series Solution of Modelling the Pollution”. Turkish Journal of Mathematics and Computer Science 13/1 (June 2021), 81-88. https://doi.org/10.47000/tjmcs.879627.
JAMA Doğan N. Series Solution of Modelling the Pollution. TJMCS. 2021;13:81–88.
MLA Doğan, Nurettin. “Series Solution of Modelling the Pollution”. Turkish Journal of Mathematics and Computer Science, vol. 13, no. 1, 2021, pp. 81-88, doi:10.47000/tjmcs.879627.
Vancouver Doğan N. Series Solution of Modelling the Pollution. TJMCS. 2021;13(1):81-8.