Staff Members - Benha University
Series solution for continuous population models for single and interacting species by the homotopy analysis method
Communications in Numerical Analysis • 2012
Publication Information
Authors
Hany N. Hassan; Magdy A. El-Tawil
Keywords
Homotopy analysis method; Convergence-controller parameter; Nonlinear differential
equations; Logistic growth; Predator-prey models.
Journal
Communications in Numerical Analysis
Publisher
Not Available
Volume
2012
Issue
Not Available
Pages
Not Available
publication.type
International
Paper Link
Not Available
Supplementary Materials
Not Available
Abstract
The homotopy analysis method (HAM) is used to find approximate analytical solutions of
continuous population models for single and interacting species. The homotopy analysis
method contains the auxiliary parameter ~, which provides us with a simple way to adjust
and control the convergence region of series solution. the solutions are compared with the
numerical results obtained using NDSolve, an ordinary differential equation solver found
in the Mathematica package and a good agreement is found. Also the solutions are com-
pared with the available analytic results obtained by other methods and more accurate
and convergent series solution found. The convergence region is also computed which
shows the validity of the HAM solution. This method is reliable and manageable.
continuous population models for single and interacting species. The homotopy analysis
method contains the auxiliary parameter ~, which provides us with a simple way to adjust
and control the convergence region of series solution. the solutions are compared with the
numerical results obtained using NDSolve, an ordinary differential equation solver found
in the Mathematica package and a good agreement is found. Also the solutions are com-
pared with the available analytic results obtained by other methods and more accurate
and convergent series solution found. The convergence region is also computed which
shows the validity of the HAM solution. This method is reliable and manageable.