In this article, Differential transform method is presented for solving Volterra’s population model for population growth of a species in a closed system. This model is a nonlinear integro-differential where the integral term represents the effect of toxin. This powerful method catches the exact solution. First Volterra’s population model has been converted to power series by one-dimensional differential transformation. Thus we obtained numerical solution Volterra’s population model.
[1]
Khatereh Tabatabaei, Department of Mathematics, Faculty of Science, Kafkas University, Kars, Turkey.
[2]
Erkan Gunerhan, Department of Computer, Faculty of Engineering, Kafkas University, Kars, Turkey.
Volterra’s Population Model, Integro-differential equation, Differential Transform Method
[1]
A. M. Wazwaz, Analytical approximations and Padé approximants for Volterra’s population model, Applied Mathematics and Computation, 100 (1999) 13-25.
[2]
J. K. Zhou, Huazhong University Press, Wuhan, China, 1986.
[3]
K. Al-Khaled, Numerical Approximations for Population Growth Models. Appl. Math. Comput, 160 (2005) 865-873.
[4]
K. Parand, M. Ghasemi ASEMI, S. Rezazadeh, A. Peiravi, A. Ghorbanpour, A. Tavakoli golpaygani, quasilinerization approach for solving Volterra’s population model, Appl. Comput. Math., (2010)95-103.
[5]
R. D. Small, Population growth in a closed system and Mathematical Modeling, in: Classroom Notes in Applied Mathematics, SIAM, Philadelphia, PA, (1989) 317-320.
[6]
S. T. Mohyud-Din, A. Yıldırım, Y. Gūlkanat, Analytical solution of Volterra’s population model, Journal of King Saud University 22 (2010) 247–250.
[7]
Arikoglu A, Ozkol I. Solution of differential?difference equations by using differential transform method. Appl. Math. Comput, 181 (2006) 153–162.
[8]
Arikoglu A, Ozkol I, Solution of fractional differential equations by using differential transform method. Chaos Soliton. Fract, 34 (2007) 1473–1481.
[9]
E. Celik, Kh. Tabatabaei, Solving a class of volterra integral equation systems by the Differential Transform Method, 9 (2010) 1-5.
[10]
V. S. Ertürk, Differential transformation method for solving differential equations of Lane-Emden type, Math. Comput. Appl, 12 (2007) 135-139.