Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2017, Cilt: 5 Sayı: 4, 89 - 96, 01.10.2017

Öz

Kaynakça

  • S. Pamuk, The decomposition method for continuous population models for single and interacting species, Appl. Math. Comput. 163 (2005) 79-88.
  • Ş. Yüzbaşı, Bessel collocation approach for solving continuous population models for single and interacting species, Appl. Math. Model. 36(8) (2012) 3787-3802.
  • H. Xu, Analytical approximations for a population growth model with fractional order, Commun. Nonlinear Sci. Numer. Simulat. 14 (2009) 1978-1983.
  • S. Momani, R. Qaralleh, Numerical approximations and Padé approximants for a fractional population growth model, Appl. Math. Model. 31 (2007) 1907-1914.
  • K.G. TeBeest, Numerical and analytical solutions of Volterra’s population model, SIAM Rev. 39 (1997) 484-93.
  • A. Gökdoğan, A. Yıldırım, M. Merdan, Solving a fractional order Model of HIV Infection of CD4+ T Cells, Math. Comput. Model. 54(9-10) (2011) 2132-2138.
  • A. Mastroberardino, Y. Cheng, A. Abdelrazec, H. Liu, Mathematical modeling of the HIV/AIDS epidemic in Cuba, Int. J. Biomath. 8(4) (2015) 1550047.
  • M. Merdan, Homotopy perturbation method for solving a model for HIV infection of CD4+ T cells, Istanb. Commerce Uni. J. Sci. 12 (2007) 39-52.
  • Ş. Yüzbaşı, M. Sezer, Bayram Kemancı, Numerical solutions of integro-differential equations and application of a population model with an improved Legendre method, Appl. Math. Model., 37(4) (2013) 2086-2101.
  • F. Shakeri, M. Dehghan, Solution of a model describing biological species living together using the variational iteration method, Math. Comput. Model. 48 (2008) 685-699.
  • Ş. Yüzbaşı, M. Sezer, An exponential approach for the system of nonlinear delay integro-differential equations describing biological species living together, Neural Comput. Appl. 27(3) (2016) 769-779.
  • G. Abramson, V.M. Kenkre, Spatiotemporal patterns in the hantavirus infection, Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66 (2002) 011912.
  • G. Abramson, V.M. Kenkre, T.L. Yates, B.R. Parmenter, Traveling waves of infection in the Hantavirus epidemics, Bull. Math. Biol. 65 (2003) 519-534.
  • Ş. Yüzbaşı, M. Sezer, An exponential matrix method for numerical solutions of Hantavirus infection model, Appl. Appl. Math. 8(1) (2013) 99-115.
  • R.C. Mittal, R. Jiwari, A Higher Order Numerical Scheme for Some Nonlinear Differential Equations: Models in Biology, Int. J. Comput. Methods Eng. Sci Mech. 12(3) (2011) 134-140.
  • Y. Khan, H.Vázquez-Leal, Q. Wu, An efficient iterated method for mathematical biology model, Neural Comput. Appl. 23 (2013) 677-682.
  • N.S. Akbar, Biomathematical study of Sutterby fluid model for blood flow in stenosed arteries, Int. J. Biomath. 8(6) (2015) 1550075.
  • A. Sohail, S. Arshad, S. Javed, K. Maqbool, Numerical analysis of fractional-order tumor model, Int. J. Biomath. 8(5) (2015) 1550069.
  • Ş. Yüzbaşı, N. Şahin, M. Sezer, Numerical solutions of systems of linear Fredholm integro-differential equations with Bessel polynomial bases. Comput. Math. Appl. 61 (2011) 3079-3096.
  • Ş. Yüzbaşı, A numerical approach for solving a class of the nonlinear Lane-Emden type equations arising in astrophysics, Math. Meth. Appl. Sci. 34 (2011) 2218-2230.
  • Ş. Yüzbaşı, N. Şahin, M. Sezer, A collocation approach for solving modelling the pollution of a system of lakes, Math. Comput. Model. 55 (2012) 330-341.
  • S.M. Goh, A.I.M. Ismail, M.S.M. Noorani, I Hashim, Dynamics of the Hantavirus infection through variational iteration method. Nonlinear Anal.-Real. 10 (2009) 2171-2176.
  • A. Gökdoğan, M. Merdan, A Yıldırım, A multistage differential transformation method for approximate solution of Hantavirus infection model, Commun. Nonlinear Sci. 17 (2012) 1-8.
  • N. Kurt, M. Çevik, Polynomial solution of the single degree of freedom system by Taylor matrix method, Mech. Res. Commun. 35 (2008) 530-536.

Bessel collocation approach for approximate solutions of Hantavirus infection model

Yıl 2017, Cilt: 5 Sayı: 4, 89 - 96, 01.10.2017

Öz

In this study, a collocation method is introduced to find the approximate solutions of Hantavirus infection model which is a system of nonlinear ordinary differential equations. The method is based on the Bessel functions of the first kind, matrix operations and collocation points. This method converts Hantavirus infection model into a matrix equation in terms of the Bessel functions of first kind, matrix operations and collocation points. The matrix equation corresponds to a system of nonlinear equations with the unknown Bessel coefficients. The reliability and efficiency of the suggested scheme are demonstrated by numerical applications and all numerical calculations have been done by using a program written in Maple.

Kaynakça

  • S. Pamuk, The decomposition method for continuous population models for single and interacting species, Appl. Math. Comput. 163 (2005) 79-88.
  • Ş. Yüzbaşı, Bessel collocation approach for solving continuous population models for single and interacting species, Appl. Math. Model. 36(8) (2012) 3787-3802.
  • H. Xu, Analytical approximations for a population growth model with fractional order, Commun. Nonlinear Sci. Numer. Simulat. 14 (2009) 1978-1983.
  • S. Momani, R. Qaralleh, Numerical approximations and Padé approximants for a fractional population growth model, Appl. Math. Model. 31 (2007) 1907-1914.
  • K.G. TeBeest, Numerical and analytical solutions of Volterra’s population model, SIAM Rev. 39 (1997) 484-93.
  • A. Gökdoğan, A. Yıldırım, M. Merdan, Solving a fractional order Model of HIV Infection of CD4+ T Cells, Math. Comput. Model. 54(9-10) (2011) 2132-2138.
  • A. Mastroberardino, Y. Cheng, A. Abdelrazec, H. Liu, Mathematical modeling of the HIV/AIDS epidemic in Cuba, Int. J. Biomath. 8(4) (2015) 1550047.
  • M. Merdan, Homotopy perturbation method for solving a model for HIV infection of CD4+ T cells, Istanb. Commerce Uni. J. Sci. 12 (2007) 39-52.
  • Ş. Yüzbaşı, M. Sezer, Bayram Kemancı, Numerical solutions of integro-differential equations and application of a population model with an improved Legendre method, Appl. Math. Model., 37(4) (2013) 2086-2101.
  • F. Shakeri, M. Dehghan, Solution of a model describing biological species living together using the variational iteration method, Math. Comput. Model. 48 (2008) 685-699.
  • Ş. Yüzbaşı, M. Sezer, An exponential approach for the system of nonlinear delay integro-differential equations describing biological species living together, Neural Comput. Appl. 27(3) (2016) 769-779.
  • G. Abramson, V.M. Kenkre, Spatiotemporal patterns in the hantavirus infection, Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66 (2002) 011912.
  • G. Abramson, V.M. Kenkre, T.L. Yates, B.R. Parmenter, Traveling waves of infection in the Hantavirus epidemics, Bull. Math. Biol. 65 (2003) 519-534.
  • Ş. Yüzbaşı, M. Sezer, An exponential matrix method for numerical solutions of Hantavirus infection model, Appl. Appl. Math. 8(1) (2013) 99-115.
  • R.C. Mittal, R. Jiwari, A Higher Order Numerical Scheme for Some Nonlinear Differential Equations: Models in Biology, Int. J. Comput. Methods Eng. Sci Mech. 12(3) (2011) 134-140.
  • Y. Khan, H.Vázquez-Leal, Q. Wu, An efficient iterated method for mathematical biology model, Neural Comput. Appl. 23 (2013) 677-682.
  • N.S. Akbar, Biomathematical study of Sutterby fluid model for blood flow in stenosed arteries, Int. J. Biomath. 8(6) (2015) 1550075.
  • A. Sohail, S. Arshad, S. Javed, K. Maqbool, Numerical analysis of fractional-order tumor model, Int. J. Biomath. 8(5) (2015) 1550069.
  • Ş. Yüzbaşı, N. Şahin, M. Sezer, Numerical solutions of systems of linear Fredholm integro-differential equations with Bessel polynomial bases. Comput. Math. Appl. 61 (2011) 3079-3096.
  • Ş. Yüzbaşı, A numerical approach for solving a class of the nonlinear Lane-Emden type equations arising in astrophysics, Math. Meth. Appl. Sci. 34 (2011) 2218-2230.
  • Ş. Yüzbaşı, N. Şahin, M. Sezer, A collocation approach for solving modelling the pollution of a system of lakes, Math. Comput. Model. 55 (2012) 330-341.
  • S.M. Goh, A.I.M. Ismail, M.S.M. Noorani, I Hashim, Dynamics of the Hantavirus infection through variational iteration method. Nonlinear Anal.-Real. 10 (2009) 2171-2176.
  • A. Gökdoğan, M. Merdan, A Yıldırım, A multistage differential transformation method for approximate solution of Hantavirus infection model, Commun. Nonlinear Sci. 17 (2012) 1-8.
  • N. Kurt, M. Çevik, Polynomial solution of the single degree of freedom system by Taylor matrix method, Mech. Res. Commun. 35 (2008) 530-536.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Şuayip Yüzbasi

Yayımlanma Tarihi 1 Ekim 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 5 Sayı: 4

Kaynak Göster

APA Yüzbasi, Ş. (2017). Bessel collocation approach for approximate solutions of Hantavirus infection model. New Trends in Mathematical Sciences, 5(4), 89-96.
AMA Yüzbasi Ş. Bessel collocation approach for approximate solutions of Hantavirus infection model. New Trends in Mathematical Sciences. Ekim 2017;5(4):89-96.
Chicago Yüzbasi, Şuayip. “Bessel Collocation Approach for Approximate Solutions of Hantavirus Infection Model”. New Trends in Mathematical Sciences 5, sy. 4 (Ekim 2017): 89-96.
EndNote Yüzbasi Ş (01 Ekim 2017) Bessel collocation approach for approximate solutions of Hantavirus infection model. New Trends in Mathematical Sciences 5 4 89–96.
IEEE Ş. Yüzbasi, “Bessel collocation approach for approximate solutions of Hantavirus infection model”, New Trends in Mathematical Sciences, c. 5, sy. 4, ss. 89–96, 2017.
ISNAD Yüzbasi, Şuayip. “Bessel Collocation Approach for Approximate Solutions of Hantavirus Infection Model”. New Trends in Mathematical Sciences 5/4 (Ekim 2017), 89-96.
JAMA Yüzbasi Ş. Bessel collocation approach for approximate solutions of Hantavirus infection model. New Trends in Mathematical Sciences. 2017;5:89–96.
MLA Yüzbasi, Şuayip. “Bessel Collocation Approach for Approximate Solutions of Hantavirus Infection Model”. New Trends in Mathematical Sciences, c. 5, sy. 4, 2017, ss. 89-96.
Vancouver Yüzbasi Ş. Bessel collocation approach for approximate solutions of Hantavirus infection model. New Trends in Mathematical Sciences. 2017;5(4):89-96.