The application of fuzzy logistic equations in population growth with parameter estimation via minimization
DOI:
https://doi.org/10.11113/mjfas.v13n2.564Abstract
This paper presents a numerical solution for the first order fuzzy logistic equations by extended Runge-Kutta fourth order method with estimated parameters. The parameters are estimated by minimization technique using conjugate gradient approach. Then, the fuzzy logistic model with the estimated parameters is used to fit the population growth in Malaysia. Numerical example is given to show the efficiency of the proposed model.
Keywords: Fuzzy logistic equations, Population growth, Parameter estimation, Minimization technique
References
Legendre, A. M., Nouvelles methodes pour la determination des orbites des comete, Paris: Courcier, 1806.
Gauss, K. F., Theory of the motion of the heavenly bodies moving about the sun in conic section, 1809, reprinted by Dover Publications, Inc., New York, 1963.
Kot M., Elements of mathematical ecology. Cambridge, UK: Cambridge University Press, 2001.
Chakrivat, P. C., Kamew, M.S., Stiffly stable second multi-step methods with higher order and improved stability regions, BIT 23, 75–83, 1983.
Enright, W. H., Second derivative multi-step methods for stiff ordinary differential equations, SIAM J. Numer. Anal. 11, 321–331, 1974.
Gear, C. W., Numerical initial value problems in ordinary differential equations, Prentice-Hall, Englewood Cliffs, NJ, 1971.
Hairer, E., Wanner, G., Solving ordinary differential equations II, Springer, Berlin, 1991.
Rosenbrock, H. H, Some general implicit processes for the numerical solution of ordinary differential equations, Computational Journal 23, 329–330, 1963.
Goeken, D., Johnson, O., Runge–Kutta with higher derivative approximations, Appl. Numer. Math. 39, 249–257, 2000.
Wu, X., Xia, J., Extended Runge–Kutta-like formulae, Application Numerical Math. 56, 1584–1605, 2006.
Mirza, A. N., Mirza, N. Q., Vlastos, G. Singletary, S. E. Prognostic factors in nodenegative breast cancer: A review of studies with sample size more than 200 and follow-up more than 5 years. Ann Surg. 235, 10 –26, 2002.
Population of Malaysia, CIA World Factbook, Retrieved on June 30, 2015.
