Numerical approximations for population growth models. (English) Zbl 1062.65142

Summary: This paper aims to introduce a comparison of the Adomian decomposition method and the Sinc-Galerkin method for the solution of some mathematical population growth models. From the computational viewpoint, the comparison shows that the Adomian decomposition method is efficient and easy to use.


65R20 Numerical methods for integral equations
45G10 Other nonlinear integral equations
92D25 Population dynamics (general)
Full Text: DOI


[1] Adomian, G., A review of the decomposition method in applied mathematics, J. math. anal. appl, 135, 501-544, (1988) · Zbl 0671.34053
[2] Adomian, G., Solving frontier problems of physics: the decomposition method, (1994), Kluwer Academic Publishers Boston, MA · Zbl 0802.65122
[3] Cherruault, Y.; Saccomandi, G.; Some, B., New results for convergence of Adomian’s method applied to integral equations, Math. comput. model, 16, 2, 85-93, (1992) · Zbl 0756.65083
[4] Greiner, G.; Heesterbeek, J.A.P.; Metz, J.A.J., A singular perturbation theorem for evaluation equations and time-scale arguments for structured population models, J. can. appl. math, Q.2, 4, 435-459, (1994) · Zbl 0828.60069
[5] Yukio, K.; Masayasu, M., Singular perturbation approach to a 3-component reaction-diffusion system arising in population dynamics, SIAM J. math. analy, 29, 6, 1519-1536, (1998) · Zbl 0920.35015
[6] Linz, P., Analytical and numerical method for Volterra equations, (1985), SIAM Philadelphia, PA · Zbl 0566.65094
[7] Lund, J.; Bowers, K.L., Sinc methods for quadrature and differential equations, (1992), SIAM Philadelphia, PA · Zbl 0753.65081
[8] Re’paci, A., Nonlinear dynamical system: on the accuracy of Adomian’s decomposition method, Appl. math. lett, 3, 4, 35-39, (1990)
[9] Scudo, F.M., Vito Volterra and theoretical ecology, Theoret. populat. biol, 2, 1-23, (1971) · Zbl 0241.92001
[10] Small, R.D.; Small, R.D., Population growth in a closed model, mathematical modelling: classroom notes in applied mathematics, J. math. anal. appl, 135, 501-544, (1988), SIAM Philadelphia, PA
[11] Stenger, F., Numerical methods based on sinc and analytic functions, (1993), Springer-Verlag New York · Zbl 0803.65141
[12] Wazwaz, A., Analytical approximations and pade’ approximations for Volterra’s population model, Appl. math. comput, 100, 13-25, (1999) · Zbl 0953.92026
[13] Williamson, M., The analysis of biological populations, (1972), Arnold London
[14] Zhanyuan, H.; cassell, J.S., Global attractivity of a single species population model, Nonlinear diff. eq. appl, 5, 2, 167-180, (1998) · Zbl 0896.34036
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.