Bessel collocation approach for solving continuous population models for single and interacting species

Abstract In this paper, we present a collocation method to obtain the approximate solutions of continuous population models for single and interacting species. By using the Bessel polynomials and collocation points, this method transforms population model into a matrix equation. The matrix equation corresponds to a system of nonlinear equations with the unknown Bessel coefficients. The reliability and efficiency of the proposed scheme are demonstrated by two numerical examples and performed on the computer algebraic system Maple.

[1]  Khosrow Maleknejad,et al.  Taylor polynomial solution of high-order nonlinear Volterra-Fredholm integro-differential equations , 2003, Appl. Math. Comput..

[2]  Mehmet Sezer,et al.  On the solution of the Riccati equation by the Taylor matrix method , 2006, Appl. Math. Comput..

[3]  Yüzbaşi.  A Collocation Approach to Solve a Class of Lane-Emden Type Equations , 2011 .

[4]  Serdal Pamuk,et al.  An application for linear and nonlinear heat equations by Adomian's decomposition method , 2005, Appl. Math. Comput..

[5]  Ji-Huan He.  A coupling method of a homotopy technique and a perturbation technique for non-linear problems , 2000 .

[6]  Handan Çerdik-Yaslan,et al.  An approximation method for the solution of nonlinear integral equations , 2006, Appl. Math. Comput..

[7]  Ji-Huan He,et al.  Homotopy perturbation method: a new nonlinear analytical technique , 2003, Appl. Math. Comput..

[8]  Ji-Huan He.  HOMOTOPY PERTURBATION METHOD FOR SOLVING BOUNDARY VALUE PROBLEMS , 2006 .

[9]  Mehmet Sezer,et al.  The approximate solution of high-order linear Volterra-Fredholm integro-differential equations in terms of Taylor polynomials , 2000, Appl. Math. Comput..

[10]  Mehmet Sezer,et al.  Numerical solutions of systems of linear Fredholm integro-differential equations with Bessel polynomial bases , 2011, Comput. Math. Appl..

[11]  Serdal Pamuk,et al.  The decomposition method for continuous population models for single and interacting species , 2005, Appl. Math. Comput..

[12]  S. Pamuk.  Solution of the porous media equation by Adomian's decomposition method , 2005 .

[13]  Mehmet Sezer,et al.  Legendre polynomial solutions of high-order linear Fredholm integro-differential equations , 2009, Appl. Math. Comput..

[14]  Mehmet Sezer,et al.  Taylor polynomial solutions of Volterra integral equations , 1994 .

[15]  Suayip Yüzbasi,et al.  A numerical approach for solving the high-order linear singular differential-difference equations , 2011, Comput. Math. Appl..

[16]  Mehmet Sezer,et al.  Chebyshev polynomial solutions of systems of higher-order linear Fredholm-Volterra integro-differential equations , 2005, J. Frankl. Inst..

[17]  Ji-Huan He.  Homotopy perturbation technique , 1999 .

[18]  Mehmet Sezer,et al.  A collocation approach to solving the model of pollution for a system of lakes , 2012, Math. Comput. Model..

[19]  Serdal Pamuk,et al.  He's homotopy perturbation method for continuous population models for single and interacting species , 2010, Comput. Math. Appl..

[20]  Mehmet Sezer,et al.  A new polynomial approach for solving difference and Fredholm integro-difference equations with mixed argument , 2005, Appl. Math. Comput..

[21]  Suayip Yüzbasi,et al.  A collocation approach for solving systems of linear Volterra integral equations with variable coefficients , 2011, Comput. Math. Appl..