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.
Volterra’s Population Model, Integro-differential equation, Differential Transform Method
A. M. Wazwaz, Analytical approximations and Padé approximants for Volterra’s population model, Applied Mathematics and Computation, 100 (1999) 13-25.
J. K. Zhou, Huazhong University Press, Wuhan, China, 1986.
K. Al-Khaled, Numerical Approximations for Population Growth Models. Appl. Math. Comput, 160 (2005) 865-873.
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.
R. D. Small, Population growth in a closed system and Mathematical Modeling, in: Classroom Notes in Applied Mathematics, SIAM, Philadelphia, PA, (1989) 317-320.
S. T. Mohyud-Din, A. Yıldırım, Y. Gūlkanat, Analytical solution of Volterra’s population model, Journal of King Saud University 22 (2010) 247–250.
Arikoglu A, Ozkol I. Solution of differential?difference equations by using differential transform method. Appl. Math. Comput, 181 (2006) 153–162.
Arikoglu A, Ozkol I, Solution of fractional differential equations by using differential transform method. Chaos Soliton. Fract, 34 (2007) 1473–1481.
E. Celik, Kh. Tabatabaei, Solving a class of volterra integral equation systems by the Differential Transform Method, 9 (2010) 1-5.
V. S. Ertürk, Differential transformation method for solving differential equations of Lane-Emden type, Math. Comput. Appl, 12 (2007) 135-139.