BibTex RIS Kaynak Göster
Yıl 2016, Cilt: 6 Sayı: 1, 150 - 162, 01.06.2016

Öz

Kaynakça

  • Adomian,G., (1983), Stochastic Systems, Academic Press, New York.
  • Adomian,G., (1988), A review of the decomposition method in applied mathematics, Journal of Math- ematical Analysis and Applications, 135, pp. 501-544.
  • Adomian,g., (1994), Solving Frontier Problems of Physics: the Decomposition Method, Kluwer, Dor- drecht.
  • Alifanov,O.M., (1994), Inverse Heat Transfer Problems. Springer, NewYork.
  • Beck,J.V., Blackwell,B. and C. R. St. Clair, (1985), Inverse Heat Conduction: IllPosed Problems. Wiley-Interscience, NewYork.
  • Cabeza,J.M.G., Garcia,J.A.M. and Rodriguez,A.C., (2005), A Sequential Algorithm of Inverse Heat Conduction Problems Using Singular Value Decomposition. International Journal of Thermal Sciences, 44, pp. 235-244.
  • Cannon,J., (1984), One dimensional heat equation. California: Addison-Wesley Publishing Company. [8] Chang,M.H., (2005), A decomposition solution for fins with temperature dependent surface heat flux, International Journal Heat and Mass Transfer, 48, pp. 1819-1824.
  • Cherruault,Y., (1989), Convergence of Adomian method, Kybernetes, 18, pp. 31-38.
  • Elden,L., (1984), A Note on the Computation of the Generalized Cross-validation Function for Ill- conditioned Least Squares Problems. BIT, 24, pp. 467-472.
  • Farcas,A. and Lesnic,D., (2006), The boundary-element method for the determination of a heat source dependent on one variable. J. Eng. Math, 54, pp. 375-388.
  • Golub,G.H., Heath,M. and Wahba,G., (1979), Generalized Cross-validation as a Method for Choosing a Good Ridge Parameter. Technometrics, 21, pp. 215-223.
  • Grzymkowski,R., Hetmaniok,E. and Sota,D., (2002), Wybrane metody obliczeniowe w rachunku wari- acyjnym oraz w rwnaniach rniczkowych i cakowych, WPKJS, Gliwice.
  • Lesnic,D., (2002), The Cauchy problem for the wave equation using the decomposition method, Ap- plied Mathematics Letters, 15, pp. 697-701.
  • Lesnic,D. and Elliott,L., (1999), The decomposition approach to inverse heat conduction, Journal of Mathematical Analysis and Applications, 232, pp. 82-98.
  • Molhem,H and Pourgholi,R., (2008), A numerical algorithm for solving a one-dimensional inverse heat conduction problem, Journal of Mathematics and Statistics, 4, pp. 60-63.
  • Murio,D.A., (1993), The Mollification Method and the Numerical Solution of Ill-Posed Problems. Wiley-Interscience, NewYork.
  • Yi,Z. and Murio,D.A., (2004), Source term identification in 1-D IHCP. Comput. Math. Appl, 47, pp. 1921-1933.
  • Murray,J.D., (1989), Mathematical Biology. Springer, Berlin.
  • Pourgholi,R. and Esfahani,A., (2013), An efficient numerical method for solving an inverse wave problem. IJCM. 10.
  • Pourgholi,R., Esfahani,A., Rahimi,H and Tabasi,S.H., (2013), Solving an inverse initial-boundary- value problem by using basis function method. Computational and Applied Mathematics, 1, pp. 27-32.
  • Pourgholi,R, Dana,H. and Tabasi,S.H., (2014), Solving an inverse heat conduction problem using ge- netic algorithm: Sequential and multi-core parallelization approach. Applied Mathematical Modelling, 38, pp. 1948-1958.
  • Pourgholi,R. and Rostamian,M., (2010), A numerical technique for solving IHCPs using Tikhonov regularization method. Applied Mathematical Modelling, 34, pp. 2102-2110.
  • Pourgholi,R., Rostamian,M. and Emamjome,M., (2010), A numerical method for solving a nonlinear inverse parabolic problem. Inverse Problems in Science and Engineering, 8, pp. 1151-1164.
  • Soufyane,A. and Boulmalf,M., (2005), Solution of linear and nonlinear parabolic equations by the decomposition method, Applied Mathematics and Computation, 162, pp. 687-693.
  • Tikhonov,A.N., Arsenin,V.Y., Winston,V.H. and Sons, (1977), Solution of Ill-Posed Problems. Wash- ington, DC.
  • Reza Pourgholi, for a photograph and biography, see TWMS Journal of Applied and Engineering Mathematics, Volume 2, No.2, 2012.

SOLVING A NONLINEAR INVERSE PROBLEM OF IDENTIFYING AN UNKNOWN SOURCE TERM IN A REACTION-DIFFUSION EQUATION BY ADOMIAN DECOMPOSITION METHOD

Yıl 2016, Cilt: 6 Sayı: 1, 150 - 162, 01.06.2016

Öz

We consider the inverse problem of finding the nonlinear source for nonlinear Reaction-Diffusion equation whenever the initial and boundary condition are given. We investigate the numerical solution of this problem by using Adomian Decomposition Method ADM . The approach of the proposed method is to approximate unknown coefficients by a nonlinear function whose coefficients are determined from the solution of minimization problem based on the overspecified data. Further, the Tikhonov regularization method is applied to deal with noisy input data and obtain a stable approximate solution. This method is tested for two examples. The results obtained show that the method is efficient and accurate. This study showed also, the speed of the convergent of ADM.

Kaynakça

  • Adomian,G., (1983), Stochastic Systems, Academic Press, New York.
  • Adomian,G., (1988), A review of the decomposition method in applied mathematics, Journal of Math- ematical Analysis and Applications, 135, pp. 501-544.
  • Adomian,g., (1994), Solving Frontier Problems of Physics: the Decomposition Method, Kluwer, Dor- drecht.
  • Alifanov,O.M., (1994), Inverse Heat Transfer Problems. Springer, NewYork.
  • Beck,J.V., Blackwell,B. and C. R. St. Clair, (1985), Inverse Heat Conduction: IllPosed Problems. Wiley-Interscience, NewYork.
  • Cabeza,J.M.G., Garcia,J.A.M. and Rodriguez,A.C., (2005), A Sequential Algorithm of Inverse Heat Conduction Problems Using Singular Value Decomposition. International Journal of Thermal Sciences, 44, pp. 235-244.
  • Cannon,J., (1984), One dimensional heat equation. California: Addison-Wesley Publishing Company. [8] Chang,M.H., (2005), A decomposition solution for fins with temperature dependent surface heat flux, International Journal Heat and Mass Transfer, 48, pp. 1819-1824.
  • Cherruault,Y., (1989), Convergence of Adomian method, Kybernetes, 18, pp. 31-38.
  • Elden,L., (1984), A Note on the Computation of the Generalized Cross-validation Function for Ill- conditioned Least Squares Problems. BIT, 24, pp. 467-472.
  • Farcas,A. and Lesnic,D., (2006), The boundary-element method for the determination of a heat source dependent on one variable. J. Eng. Math, 54, pp. 375-388.
  • Golub,G.H., Heath,M. and Wahba,G., (1979), Generalized Cross-validation as a Method for Choosing a Good Ridge Parameter. Technometrics, 21, pp. 215-223.
  • Grzymkowski,R., Hetmaniok,E. and Sota,D., (2002), Wybrane metody obliczeniowe w rachunku wari- acyjnym oraz w rwnaniach rniczkowych i cakowych, WPKJS, Gliwice.
  • Lesnic,D., (2002), The Cauchy problem for the wave equation using the decomposition method, Ap- plied Mathematics Letters, 15, pp. 697-701.
  • Lesnic,D. and Elliott,L., (1999), The decomposition approach to inverse heat conduction, Journal of Mathematical Analysis and Applications, 232, pp. 82-98.
  • Molhem,H and Pourgholi,R., (2008), A numerical algorithm for solving a one-dimensional inverse heat conduction problem, Journal of Mathematics and Statistics, 4, pp. 60-63.
  • Murio,D.A., (1993), The Mollification Method and the Numerical Solution of Ill-Posed Problems. Wiley-Interscience, NewYork.
  • Yi,Z. and Murio,D.A., (2004), Source term identification in 1-D IHCP. Comput. Math. Appl, 47, pp. 1921-1933.
  • Murray,J.D., (1989), Mathematical Biology. Springer, Berlin.
  • Pourgholi,R. and Esfahani,A., (2013), An efficient numerical method for solving an inverse wave problem. IJCM. 10.
  • Pourgholi,R., Esfahani,A., Rahimi,H and Tabasi,S.H., (2013), Solving an inverse initial-boundary- value problem by using basis function method. Computational and Applied Mathematics, 1, pp. 27-32.
  • Pourgholi,R, Dana,H. and Tabasi,S.H., (2014), Solving an inverse heat conduction problem using ge- netic algorithm: Sequential and multi-core parallelization approach. Applied Mathematical Modelling, 38, pp. 1948-1958.
  • Pourgholi,R. and Rostamian,M., (2010), A numerical technique for solving IHCPs using Tikhonov regularization method. Applied Mathematical Modelling, 34, pp. 2102-2110.
  • Pourgholi,R., Rostamian,M. and Emamjome,M., (2010), A numerical method for solving a nonlinear inverse parabolic problem. Inverse Problems in Science and Engineering, 8, pp. 1151-1164.
  • Soufyane,A. and Boulmalf,M., (2005), Solution of linear and nonlinear parabolic equations by the decomposition method, Applied Mathematics and Computation, 162, pp. 687-693.
  • Tikhonov,A.N., Arsenin,V.Y., Winston,V.H. and Sons, (1977), Solution of Ill-Posed Problems. Wash- ington, DC.
  • Reza Pourgholi, for a photograph and biography, see TWMS Journal of Applied and Engineering Mathematics, Volume 2, No.2, 2012.
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

R. Pourgholi Bu kişi benim

A. Saeedi Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 6 Sayı: 1

Kaynak Göster