Solusi Model Merokok Menggunakan Metode Perturbasi Homotopi
Abstract
Artikel ini meninjau masalah dinamika perilaku merokok. Metode perturbasi homotopi diterapkan untuk menghitung solusi sistem persamaan differensial pada masalah tersebut. Hasil ini kemudian dibandingkan dengan hasil dari metode numerik. Hasil menunjukkan bahwa solusi metode perturbasi homotopi cenderung menghasilkan kecocokan yang baik terhadap solusi numerik pada beberapa selang waktu.
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D. C. Rowe, L. Chassin, C. C. Presson, D. Edwards, and S. J. Sherman, “An ‘epidemic’ model of adolescent cigarette smoking,” Journal of applied social psychology, vol. 22, no. 4, pp. 261–285, 1992.
F. Brauer, C. Castillo-Chavez, and C. Castillo-Chavez, Mathematical models in population biology and epidemiology, vol. 40. Springer, 2001.
C. Castillo-Garsow, G. Jordan-Salivia, and A. R. Herrera, “Mathematical models for the dynamics of tobacco use, recovery,” and relapse, 2000.
O. Sharomi and A. B. Gumel, “Curtailing smoking dynamics: a mathematical modeling approach,” Applied Mathematics and Computation, vol. 195, no. 2, pp. 475–499, 2008.
A. Lahrouz, L. Omari, D. Kiouach, and A. Belmaâti, “Deterministic and stochastic stability of a mathematical model of smoking,” Statistics & Probability Letters, vol. 81, no. 8, pp. 1276–1284, 2011.
G. Zaman, “Qualitative behavior of giving up smoking models,” Bulletin of the Malaysian Mathematical Sciences Society, vol. 34, no. 2, pp. 403–415, 2011.
A. Zeb, G. Zaman, and S. Momani, “Square-root dynamics of a giving up smoking model,” Applied Mathematical Modelling, vol. 37, no. 7, pp. 5326–5334, 2013.
L. Pang, Z. Zhao, S. Liu, and X. Zhang, “A mathematical model approach for tobacco control in China,” Applied Mathematics and Computation, vol. 259, pp. 497–509, 2015.
A. Yadav, P. K. Srivastava, and A. Kumar, “Mathematical model for smoking: Effect of determination and education,” International Journal of Biomathematics, vol. 8, no. 01, p. 1550001, 2015.
J.-H. He, “A coupling method of a homotopy technique and a perturbation technique for non-linear problems,” International Journal of Non-Linear Mechanics, vol. 35, no. 1, pp. 37–43, 2000.
M. Rafei, H. Daniali, D. D. Ganji, and H. Pashaei, “Solution of the prey and predator problem by homotopy perturbation method,” Applied Mathematics and Computation, vol. 188, no. 2, pp. 1419–1425, 2007.
M. Rafei, D. D. Ganji, and H. Daniali, “Solution of the epidemic model by homotopy perturbation method,” Applied Mathematics and Computation, vol. 187, no. 2, pp. 1056–1062, 2007.
H. Aminikhah, “The combined Laplace transform and new homotopy perturbation methods for stiff systems of ODEs,” Applied Mathematical Modelling, vol. 36, no. 8, pp. 3638–3644, 2012.
H. Aminikhah and M. Hemmatnezhad, “An effective modification of the homotopy perturbation method for stiff systems of ordinary differential equations,” Applied Mathematics Letters, vol. 24, no. 9, pp. 1502–1508, 2011.
J. Biazar, M. A. Asadi, and F. Salehi, “Rational Homotopy Perturbation Method for solving stiff systems of ordinary differential equations,” Applied Mathematical Modelling, vol. 39, no. 3, pp. 1291–1299, 2015.
O. Abdulaziz, I. Hashim, and S. Momani, “Solving systems of fractional differential equations by homotopy-perturbation method,” Physics Letters A, vol. 372, no. 4, pp. 451–459, 2008.
J. Biazar, H. Ghazvini, and M. Eslami, “He’s homotopy perturbation method for systems of integro-differential equations,” Chaos, Solitons & Fractals, vol. 39, no. 3, pp. 1253–1258, 2009.
P. Roul and P. Meyer, “Numerical solutions of systems of nonlinear integro-differential equations by Homotopy-perturbation method,” Applied Mathematical Modelling, vol. 35, no. 9, pp. 4234–4242, 2011.
J. Biazar and M. Eslami, “A new homotopy perturbation method for solving systems of partial differential equations,” Computers & Mathematics with Applications, vol. 62, no. 1, pp. 225–234, 2011.
Jaharuddin, “Homotopy perturbation method for a SEIR model with varying total population size,” Far East Journal of Mathematical Sciences, vol. 2, 2014.
M. Suleman, Q. Wu, and G. Abbas, “Approximate analytic solution of (2+1) dimensional coupled differential Burger’s equation using Elzaki Homotopy Perturbation Method,” Alexandria Engineering Journal, vol. 55, no. 2, pp. 1817–1826, 2016.
M. H. Tiwana, K. Maqbool, and A. B. Mann, “Homotopy perturbation Laplace transform solution of fractional non-linear reaction diffusion system of Lotka-Volterra type differential equation,” Engineering Science and Technology, an International Journal, vol. 20, no. 2, pp. 672–678, 2017.
C. R. B. Moutsinga, E. Pindza, and E. Maré, “Homotopy perturbation transform method for pricing under pure diffusion models with affine coefficients,” Journal of King Saud University - Science, vol. 30, no. 1, pp. 1–13, 2018.
DOI: http://dx.doi.org/10.12962/limits.v18i2.6479
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Limits: Journal Mathematics and its Aplications by Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at https://iptek.its.ac.id/index.php/limits.