Araştırma Makalesi
BibTex RIS Kaynak Göster

A Weighted Algorithm for Solving a Cauchy Problem of The Sideways Parabolic Equation

Yıl 2018, Cilt: 8, 1 - 9, 30.06.2018

Öz

In this paper, a weighted algorithm based on the reduced differential transform method is presented for
solving some sideways parabolic equations. The proposed approach uses initial and boundary conditions simultaneously
for obtaining an approximate analytical solution of equation. A description of the algorithm to solve the
problem and determining the boundary condition is given. Finally, some examples are discussed to show ability of
the presented algorithm and to confirm utility of this method.

Kaynakça

  • Adomian, G., Application of decomposition to convection-diffusion equations, Appl. Math. Lett., 1(1988), 7–9.
  • Arikoglu, A., Ozkol, I., Solution of integro-differential equation systems by using di erential transform method, Computer and Mathematics with Applications, 56(2008), 2411–2417.
  • Babaei, A., Mohammadpour, A., Solving an inverse heat conduction problem by reduced di erential transform method, New trends in Mathematical sciences, 3(2015), 65–70.
  • Bazan, F. S. V., Chebyshev pseudospectral method for computing numerical solution of convection-di usion equation, Applied Mathematics and Computation, 200(2)(2008), 537–546.
  • Beck, J. V., Blackwell, B., Chair, S.R., Inverse Heat Conduction: III-Posed Problems, Wiley, New York, 1985.
  • Berntsson, F., A spectral method for solving the sideways heat equation, Inverse Problems, 15(1999), 891–906.
  • Blom, E., Nyqvist, P., Loyd, D., Suction Pyrometer Analysis of The Instrument and Guide for Users, Varmeforsk, 2004.
  • Carasso, A., Determining surface temperatures from interior observations, SIAM J. Appl. Math., 42(1982), 558–574.
  • Chertock, A., Kurganov, A., On Splitting-Based Numerical Methods for Convection-Diffusion Equations, Quaderni di Matematica, 24(2009), 303–343.
  • Deng, Y., Liu, Z., Iteration methods on sideways parabolic equations, Inverse Problems, 25(9)(2009), 095004 (14pp).
  • Golz, W. J., Dorroh, J.R., The convection-di usion equation for a finite domain with time varying boundaries, APPL MATH L, 14(8)(2001), 983–988.
  • Hao, D. N., Reinhard, H. J., On a sideways parabolic equation, Inverse Problems, 13(1997), 297–309.
  • Karalashvili, M., Gros, S., Mhamdi, A., Reusken, A., Marquardt, W., Identification of transport cofficient models in convection-diffusion equations, SIAM J. Sci. Comput., 33(2011), 303–327.
  • Keskin, Y., Oturanc, G., Reduced differential transform method for partial differential equations, International Journal of Nonlinear Sciences and Numerical Simulation, 10(2)(2009), 7414–749.
  • Kurnaz, A., Oturance, G., The differential transform approximation for the system of ordinary differential equations, International Journal of Computer Mathematics, 82(6)(2005), 709–719.
  • Lesnic, D., The decomposition method for Cauchy advection-diffusion problems, Comput. Math. Appl., 49(2005), 525–537.
  • Regiriska, T., Sideways heat equation and wavelets, J. Comput. Appl. Math., 63(1995), 209–214.
  • Shidfar, A., Garshasbi, M., A weighted algorithm based on Adomian decomposition method for solving an special class of evolution equations, Commun. Nonlinear Sci. Numer. Simulat., 14(2009), 1146–1151.
  • Tautenhahn, U., Optimal stable approximations for the sideways heat equation, J. Inv. Ill-Posed Probs, 5(1997), 287–307.
  • Wang, J., The multi-resolution method applied to the sideways heat equation, Journal of Mathematical Analysis and Applications, 309(2005), 661– 673.
  • Zhou, J. K., Differential transform and its applications for Electrical Circuits, Huazhong University Press, Wuhan, China, 1986.
Yıl 2018, Cilt: 8, 1 - 9, 30.06.2018

Öz

Kaynakça

  • Adomian, G., Application of decomposition to convection-diffusion equations, Appl. Math. Lett., 1(1988), 7–9.
  • Arikoglu, A., Ozkol, I., Solution of integro-differential equation systems by using di erential transform method, Computer and Mathematics with Applications, 56(2008), 2411–2417.
  • Babaei, A., Mohammadpour, A., Solving an inverse heat conduction problem by reduced di erential transform method, New trends in Mathematical sciences, 3(2015), 65–70.
  • Bazan, F. S. V., Chebyshev pseudospectral method for computing numerical solution of convection-di usion equation, Applied Mathematics and Computation, 200(2)(2008), 537–546.
  • Beck, J. V., Blackwell, B., Chair, S.R., Inverse Heat Conduction: III-Posed Problems, Wiley, New York, 1985.
  • Berntsson, F., A spectral method for solving the sideways heat equation, Inverse Problems, 15(1999), 891–906.
  • Blom, E., Nyqvist, P., Loyd, D., Suction Pyrometer Analysis of The Instrument and Guide for Users, Varmeforsk, 2004.
  • Carasso, A., Determining surface temperatures from interior observations, SIAM J. Appl. Math., 42(1982), 558–574.
  • Chertock, A., Kurganov, A., On Splitting-Based Numerical Methods for Convection-Diffusion Equations, Quaderni di Matematica, 24(2009), 303–343.
  • Deng, Y., Liu, Z., Iteration methods on sideways parabolic equations, Inverse Problems, 25(9)(2009), 095004 (14pp).
  • Golz, W. J., Dorroh, J.R., The convection-di usion equation for a finite domain with time varying boundaries, APPL MATH L, 14(8)(2001), 983–988.
  • Hao, D. N., Reinhard, H. J., On a sideways parabolic equation, Inverse Problems, 13(1997), 297–309.
  • Karalashvili, M., Gros, S., Mhamdi, A., Reusken, A., Marquardt, W., Identification of transport cofficient models in convection-diffusion equations, SIAM J. Sci. Comput., 33(2011), 303–327.
  • Keskin, Y., Oturanc, G., Reduced differential transform method for partial differential equations, International Journal of Nonlinear Sciences and Numerical Simulation, 10(2)(2009), 7414–749.
  • Kurnaz, A., Oturance, G., The differential transform approximation for the system of ordinary differential equations, International Journal of Computer Mathematics, 82(6)(2005), 709–719.
  • Lesnic, D., The decomposition method for Cauchy advection-diffusion problems, Comput. Math. Appl., 49(2005), 525–537.
  • Regiriska, T., Sideways heat equation and wavelets, J. Comput. Appl. Math., 63(1995), 209–214.
  • Shidfar, A., Garshasbi, M., A weighted algorithm based on Adomian decomposition method for solving an special class of evolution equations, Commun. Nonlinear Sci. Numer. Simulat., 14(2009), 1146–1151.
  • Tautenhahn, U., Optimal stable approximations for the sideways heat equation, J. Inv. Ill-Posed Probs, 5(1997), 287–307.
  • Wang, J., The multi-resolution method applied to the sideways heat equation, Journal of Mathematical Analysis and Applications, 309(2005), 661– 673.
  • Zhou, J. K., Differential transform and its applications for Electrical Circuits, Huazhong University Press, Wuhan, China, 1986.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Afshin Babaei

Alireza Mohammadpour

Yayımlanma Tarihi 30 Haziran 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 8

Kaynak Göster

APA Babaei, A., & Mohammadpour, A. (2018). A Weighted Algorithm for Solving a Cauchy Problem of The Sideways Parabolic Equation. Turkish Journal of Mathematics and Computer Science, 8, 1-9.
AMA Babaei A, Mohammadpour A. A Weighted Algorithm for Solving a Cauchy Problem of The Sideways Parabolic Equation. TJMCS. Haziran 2018;8:1-9.
Chicago Babaei, Afshin, ve Alireza Mohammadpour. “A Weighted Algorithm for Solving a Cauchy Problem of The Sideways Parabolic Equation”. Turkish Journal of Mathematics and Computer Science 8, Haziran (Haziran 2018): 1-9.
EndNote Babaei A, Mohammadpour A (01 Haziran 2018) A Weighted Algorithm for Solving a Cauchy Problem of The Sideways Parabolic Equation. Turkish Journal of Mathematics and Computer Science 8 1–9.
IEEE A. Babaei ve A. Mohammadpour, “A Weighted Algorithm for Solving a Cauchy Problem of The Sideways Parabolic Equation”, TJMCS, c. 8, ss. 1–9, 2018.
ISNAD Babaei, Afshin - Mohammadpour, Alireza. “A Weighted Algorithm for Solving a Cauchy Problem of The Sideways Parabolic Equation”. Turkish Journal of Mathematics and Computer Science 8 (Haziran 2018), 1-9.
JAMA Babaei A, Mohammadpour A. A Weighted Algorithm for Solving a Cauchy Problem of The Sideways Parabolic Equation. TJMCS. 2018;8:1–9.
MLA Babaei, Afshin ve Alireza Mohammadpour. “A Weighted Algorithm for Solving a Cauchy Problem of The Sideways Parabolic Equation”. Turkish Journal of Mathematics and Computer Science, c. 8, 2018, ss. 1-9.
Vancouver Babaei A, Mohammadpour A. A Weighted Algorithm for Solving a Cauchy Problem of The Sideways Parabolic Equation. TJMCS. 2018;8:1-9.