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Rational approximations for solving cauchy problems

Yıl 2016, Cilt: 4 Sayı: 3, 254 - 262, 30.09.2016

Öz



In this letter, numerical solutions of Cauchy problems
are considered by multivariate Padé approximations (MPA). Multivariate Padé
approximations (MPA) were applied to power series solutions of Cauchy problems
that solved by using He’s variational iteration method (VIM). Then, numerical
results obtained by using multivariate Padé approximations were compared with
the exact solutions of Cauchy problems.




Kaynakça

  • N. Guzel, M. Bayram, On the numerical solution of differential-algebraic equations with index-3, Applied Mathematics and Computation (2006), 175(2), 1320-1331. E. Celik, M. Bayram, http://www.sciencedirect.com/science/article/pii/S0096300303007197Numerical solution of differential–algebraic equation systems and applications, Applied Mathematics and Computation (2004), 154 ( 2): 405-413.
  • V. Turut and N Guzel., Comparing Numerical Methods for Solving Time- Fractional Reaction-Diffusion Equations, ISRN Mathematical Analysis (2012), Doi:10.5402/2012/737206.
  • V. Turut, N. Güzel, Multivariate padé approximation for solving partial differential equations of fractional order”,Abstract and Applied Analysis (2013), in press.
  • V. Turut, E. Çelik, M. Yiğider, Multivariate padé approximation for solving partial differential equations (PDE), International Journal For Numerical Methods In Fluids (2011), 66 (9):1159-1173. X. W. Zhou, L. Yao, http://www.sciencedirect.com/science/article/pii/S0898122110003718The variational iteration method for Cauchy problems, Computers & Mathematics with Applications (2010), 60 ( 3): 756-760. J.H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Eng. (1998), 167: 57-68.
  • J.H. He, Variational iteration method-a kind of non-linear analytical technique: some examples, Int. J. Non-Linear. Mech. (1999), 34: 699-708. J.H. He, Variational iteration method-some recent results and new interpretations, J. Comput. Appl. Math. (2007), 207: 3-17. J.H. He, X.H. Wu, Variational iteration method: new development and applications, Comput. Math. Appl. (2007), 54: 881-894. J.H. He, G.-C. Wu, F. Austin, The variational iteration method which should be followed, Nonlinear Sci. Lett. A (2010), 1: 1-30.
  • A. Cuyt, L. Wuytack, Nonlinear Methods in Numerical Analysis, Elsevier Science Publishers B.V. (1987), Amsterdam Abdul-Majid Wazwaz, Partial Differential Equations and Solitary Waves Theory, Higher Education Press (2009), Beijing G. Baker , P. Graves-Morris ,Padé Approximants. Basic Theory. Encyclopedia of Mathematics and its applications: vol 13., Addison- Wpsley, Reading (1981), Massachusetts.
  • A. Cuyt, A multivariate convergence theorem of the “de Montessus de Ballore” type, J. Comput. Appl. Math. (1990), 32: 47-57.
  • A. Cuyt, K. Driver and D.S. Lubinsky, Nuttall-Pommerenke theorem for homogeneous Padé approximants, J. Comput. Appl. Math. (1996), 67: 141-146. A. Cuyt, K. Driver and D.S. Lubinsky, A direct approach to convergence of multivariate, non-homogeneous, Padé approximants, J. Comput. Appl. Math. (1996), 69: 353-366.
  • C. Brezinski, Extrapolation algorithms and Padé approximations: a historical survey, Appl. Numer. Math. (1996), 20: 299-318.
Yıl 2016, Cilt: 4 Sayı: 3, 254 - 262, 30.09.2016

Öz

Kaynakça

  • N. Guzel, M. Bayram, On the numerical solution of differential-algebraic equations with index-3, Applied Mathematics and Computation (2006), 175(2), 1320-1331. E. Celik, M. Bayram, http://www.sciencedirect.com/science/article/pii/S0096300303007197Numerical solution of differential–algebraic equation systems and applications, Applied Mathematics and Computation (2004), 154 ( 2): 405-413.
  • V. Turut and N Guzel., Comparing Numerical Methods for Solving Time- Fractional Reaction-Diffusion Equations, ISRN Mathematical Analysis (2012), Doi:10.5402/2012/737206.
  • V. Turut, N. Güzel, Multivariate padé approximation for solving partial differential equations of fractional order”,Abstract and Applied Analysis (2013), in press.
  • V. Turut, E. Çelik, M. Yiğider, Multivariate padé approximation for solving partial differential equations (PDE), International Journal For Numerical Methods In Fluids (2011), 66 (9):1159-1173. X. W. Zhou, L. Yao, http://www.sciencedirect.com/science/article/pii/S0898122110003718The variational iteration method for Cauchy problems, Computers & Mathematics with Applications (2010), 60 ( 3): 756-760. J.H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Eng. (1998), 167: 57-68.
  • J.H. He, Variational iteration method-a kind of non-linear analytical technique: some examples, Int. J. Non-Linear. Mech. (1999), 34: 699-708. J.H. He, Variational iteration method-some recent results and new interpretations, J. Comput. Appl. Math. (2007), 207: 3-17. J.H. He, X.H. Wu, Variational iteration method: new development and applications, Comput. Math. Appl. (2007), 54: 881-894. J.H. He, G.-C. Wu, F. Austin, The variational iteration method which should be followed, Nonlinear Sci. Lett. A (2010), 1: 1-30.
  • A. Cuyt, L. Wuytack, Nonlinear Methods in Numerical Analysis, Elsevier Science Publishers B.V. (1987), Amsterdam Abdul-Majid Wazwaz, Partial Differential Equations and Solitary Waves Theory, Higher Education Press (2009), Beijing G. Baker , P. Graves-Morris ,Padé Approximants. Basic Theory. Encyclopedia of Mathematics and its applications: vol 13., Addison- Wpsley, Reading (1981), Massachusetts.
  • A. Cuyt, A multivariate convergence theorem of the “de Montessus de Ballore” type, J. Comput. Appl. Math. (1990), 32: 47-57.
  • A. Cuyt, K. Driver and D.S. Lubinsky, Nuttall-Pommerenke theorem for homogeneous Padé approximants, J. Comput. Appl. Math. (1996), 67: 141-146. A. Cuyt, K. Driver and D.S. Lubinsky, A direct approach to convergence of multivariate, non-homogeneous, Padé approximants, J. Comput. Appl. Math. (1996), 69: 353-366.
  • C. Brezinski, Extrapolation algorithms and Padé approximations: a historical survey, Appl. Numer. Math. (1996), 20: 299-318.
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Veyis Turut

Mustafa Bayram

Yayımlanma Tarihi 30 Eylül 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 3

Kaynak Göster

APA Turut, V., & Bayram, M. (2016). Rational approximations for solving cauchy problems. New Trends in Mathematical Sciences, 4(3), 254-262.
AMA Turut V, Bayram M. Rational approximations for solving cauchy problems. New Trends in Mathematical Sciences. Eylül 2016;4(3):254-262.
Chicago Turut, Veyis, ve Mustafa Bayram. “Rational Approximations for Solving Cauchy Problems”. New Trends in Mathematical Sciences 4, sy. 3 (Eylül 2016): 254-62.
EndNote Turut V, Bayram M (01 Eylül 2016) Rational approximations for solving cauchy problems. New Trends in Mathematical Sciences 4 3 254–262.
IEEE V. Turut ve M. Bayram, “Rational approximations for solving cauchy problems”, New Trends in Mathematical Sciences, c. 4, sy. 3, ss. 254–262, 2016.
ISNAD Turut, Veyis - Bayram, Mustafa. “Rational Approximations for Solving Cauchy Problems”. New Trends in Mathematical Sciences 4/3 (Eylül 2016), 254-262.
JAMA Turut V, Bayram M. Rational approximations for solving cauchy problems. New Trends in Mathematical Sciences. 2016;4:254–262.
MLA Turut, Veyis ve Mustafa Bayram. “Rational Approximations for Solving Cauchy Problems”. New Trends in Mathematical Sciences, c. 4, sy. 3, 2016, ss. 254-62.
Vancouver Turut V, Bayram M. Rational approximations for solving cauchy problems. New Trends in Mathematical Sciences. 2016;4(3):254-62.