An improved numerical method for a class of astrophysics problems based on radial basis functions

Physica Scripta

Volumn 83, Issue 1, 2011, Pages

  Parand, K ^a   Abbasbandy, S ^b   Kazem, S ^b   Rezaei, A R ^a  

^a SHAHID BEHESHTI UNIVERSITY   (Iran)

^b IMAM KHOMEINI INTERNATIONAL UNIVERSITY   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

COLLOCATION POINTS; CONVERGENCE RATES; RADIAL BASIS FUNCTIONS; SEMI-INFINITE DOMAINS; TEST EXAMPLES;

NONLINEAR EQUATIONS; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS; RADIAL BASIS FUNCTION NETWORKS;

ASTROPHYSICS;

EID: 78751558362     PISSN: 00318949     EISSN: 14024896     Source Type: Journal    
DOI: 10.1088/0031-8949/83/01/015011     Document Type: Article

References (66)

1. Abbasbandy S and Shivanian E 2010 Prediction of multiplicity of solutions of nonlinear boundary value problems: novel application of homotopy analysis method Commun. Nonlinear Sci. Numer. Simul. 15 3830-46
2. Abbasbandy S and Shirzadi A 2008 The variational iteration method for a class of eighth-order boundary-value differential equations Z. Nat. forsch. A 63 745-51
3. Parand K, Rezaei A R and Taghavi A 2010 Lagrangian method for solving Lane-Emden type equation arising in astrophysics on semi-infinite domains Acta Astronaut. 67 673-80
4. Parand K, Rezaei A R and Taghavi A 2010 Numerical approximations for population growth model by rational Chebyshev and Hermite functions collocation approach: a comparison Math. Methods Appl. Sci. 33 2076-86
5. Abbasbandy S and Shivanian E 2010 Exact analytical solution of a nonlinear equation arising in heat transfer Phys. Lett. A 374 567-74
6. Parand K, Dehghan M, Rezaei A R and Ghaderi S M 2010 An approximation algorithm for the solution of the nonlinear Lane-Emden-type equations arising in astrophysics using Hermite functions collocation method Comput. Phys. Commun. 6 1096-108
7. Parand K, Rezaei A R and Ghaderi S M 2011 An approximate solution of the MHD Falkner-Skan flow by Hermite functions pseudospectral method Commun. Nonlinear Sci. Numer. Simul. 1 274-83
8. Coulaud O, Funaro D and Kavian O 1990 Laguerre spectral approximation of elliptic problems in exterior domains Comput. Method. Appl. Mech. Eng. 80 451-8
9. Funaro D and Kavian O Approximation of some diffusion evolution equations in unbounded domains by Hermite functions Math. Comput. 57 597-619
10. Funaro D 1999 Computational aspects of pseudospectral Laguerre approximations Math. Comput. 6 447-57
11. Guo B Y 1999 Error estimation of Hermite spectral method for nonlinear partial differential equations Math. Comput. 68 1067-78
12. Guo B Y and Shen J 2000 Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval Numer. Mathods 86 635-54
13. Maday Y, Pernaud-Thomas B and Vandeven H 1985 Reappraisal of Laguerre type spectral methods Rech. Aerosp. 6 13-35
14. Shen J 2000 Stable and efficient spectral methods in unbounded domains using Laguerre functions SIAM J. Numer. Anal. 38 1113-33
15. Siyyam H I 2001 Laguerre tau methods for solving higher order ordinary differential equations J. Comput. Anal. Appl. 3 173-82
16. Chandrasekhar S 1967 Introduction to the Study of Stellar Structure (New York: Dover)
17. Davis H T 1962 Introduction to Nonlinear Differential and Integral Equations (New York: Dover)
18. Bender C M, Milton K A, Pinsky S S and Simmons L M Jr 1989 A new perturbative approach to nonlinear problems J. Math. Phys. 30 1447-55
19. Mandelzweig V B and Tabakin F 2001 Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs Comput. Phys. Commun. 141 268-81
20. Shawagfeh N T 1993 Nonperturbative approximate solution for Lane-Emden equation J. Math. Phys. 34 4364-9
21. Wazwaz A 2001 A new algorithm for solving differential equations of Lane-Emden type Appl. Math. Comput. 118 287-310
22. Wazwaz A 2006 The modified decomposition method for analytic treatment of differential equations Appl. Math. Comput. 173 165-76
23. Liao S 2003 A new analytic algorithm of Lane-Emden type equations Appl. Math. Comput. 142 1-16
24. He J H 2003 Variational approach to the Lane-Emden equation Appl. Math. Comput. 143 539-41
25. Ramos J I 2003 Linearization methods in classical and quantum mechanics Comput. Phys. Commun. 153 199-208
26. Parand K and Razzaghi M 2004 Rational Legendre approximation for solving some physical problems on semi-infinite intervals Phys. Scr. 69 353
27. Parand K, Shahini M and Dehghan M 2009 Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane-Emden type J. Comput. Phys. 228 8830-40
28. Parand K and Pirkhedri A 2010 Sinc-Collocation method for solving astrophysics equations New Astron. 15 533-7
29. Ramos J I 2005 Linearization techniques for singular initial-value problems of ordinary differential equations Appl. Math. Comput. 161 525-42
30. Ramos J I 2009 Piecewise-adaptive decomposition methods Chaos Solitons Fractals 40 1623-36
31. Ramos J I 2008 Series approach to the Lane-Emden equation and comparison with the homotopy perturbation method Chaos Solitons Fractals 38 400-8
32. Yousefi S A 2006 Legendre wavelets method for solving differential equations of Lane-Emden type Appl. Math. Comput. 181 1417-22
33. Bataineh A S, Noorani M S M and Hashim I 2009 Solutions of a class of singular second-order IVPs by homotopy-perturbation method Commun. Nonlinear. Sci. Numer. Simul. 14 1121-31
34. Chowdhury M S H and Hashim I 2009 Solutions of Emden-Fowler equations by homotopy perturbation method Nonlinear Anal. Real World Appl. 10 104-15
35. Aslanov A 2008 Determination of convergence intervals of the series solutions of Emden-Fowler equations using polytropes and isothermal spheres Phys. Lett. A 372 3555-61
36. Dehghan M and Shakeri F 2008 Approximate solution of a differential equation arising in astrophysics using the variational iteration method New. Astron. 13 53-9
37. Kara A H and Mahomed F M 1992 Equivalent Lagrangians and solutions of some classes of nonlinear equations Int. J. Nonlinear Mech. 27 919-27
38. Kara A H and Mahomed F M 1993 A note on the solutions of the Emden-Fowler equation Int. J. Nonlinear Mech. 28 379-84
39. Parand K, Abbasbandy S, Kazem S and Rezaei A R 2010 Comparison between two comm on collocation approaches based on radial basis functions for the case of heat transfer equations arising in porous medium Commun. Nonlinear Sci. Numer. Simul. 16 1396-407
40. Dehghan M and Shokri A 2009 A meshless method for numerical solution of the one-dimensional wave equation with an integral condition using radial basis functions Numer. Algorithms 52 461-77
41. Abbasbandy S 2006 The application of homotopy analysis method to nonlinear equations arising in heat transfer Phys. Lett. A 360 109-13
42. Mai-Duy N 2005 Solving high order ordinary differential equations with radial basis function networks Int. J. Numer. Methods Eng. 62 824-52 (Pubitemid 40195781)
43. Kansa E J 1990 Multiquadrics-a scattered data approximation scheme with applications to computational fluid dynamics - II. Solutions to parabolic, hyperbolic and elliptic partial differential equations Comput. Math. Appl. 19 147-61
44. Zerroukat M, Power H and Chen C S 1998 A numerical method for heat transfer problems using collocation and radial basis functions Int. J. Numer. Methods Eng. 42 1263-78
45. Mai-Duy N and Tran-Cong T 2001 Numerical solution of differential equations using multiquadric radial basis function networks Neural Netw. 14 185-99 (Pubitemid 32157010)
46. Mai-Duy N and Tran-Cong T 2001 Numerical solution of Navier-Stokes equations using multiquadric radial basis function networks Int. J. Numer. Methods Fluids 37 65-86 (Pubitemid 32826617)
47. Fornberg B 2008 Comparisons between pseudospectral and radial basis function derivative approximations IMA J. Numer. Anal. 30 149-72
48. Mai-Duy N and Tran-Cong T 2003 Approximation of function and its derivatives using radial basis function network methods Appl. Math. Modelling 27 197-220
49. Golberg M A, Chen C S and Bowman H 1999 Some recent results and proposals for the use of radial basis functions in the BEM Eng. Anal. Bound. Elem. 23 285-96
50. Powell M J D 1992 The Theory of Radial Basis Function Approximation in 1990 (Oxford: Clarendon)
51. Sarra S A 2005 Adaptive radial basis function method for time dependent partial differential equations Appl. Numer. Math. 54 79-94
52. 2 in multiquadric interpolation Comput. Math. Appl. 21 29-42
53. Rippa S 1999 An algorithm for selecting a good parameter c in radial basis function interpolation Adv. Comput. Math. 11 193-210
54. Fornberg B, Dirscol T, Wright G and Charles R 2002 Observations on the behavior of radial basis function approximations near boundaries Comput. Math. Appl. 43 473-90
55. Buhmann M D 2003 Radial Basis Functions: Theory and Implementations (Cambridge: Cambridge University Press)
56. Wu Z M 2002 Radial basis function scattered data interpolation and the meshless method of numerical solution of PDEs J. Eng. Math. 19 1-12
57. Wu Z M and Schaback R 1993 Local error estimates for radial basis function interpolation of scattered data IMA J. Numer. Anal. 13 13-27
58. Wendland H 2005 Scattered Data Approximation (Cambridge: Cambridge University Press)
59. Fasshauer G F 2007 Meshfree Approximation Methods with MATLAB (Singapore: World Scientific)
60. Boyd J P and Bridge L R 2010 Sensitivity of RBF interpolation on an otherwise uniform grid with a point omitted or slightly shifted Appl. Numer. Math. 60 659-72
61. Chowdhury M S H and Hashim I 2007 Homotopy analysis method for singular IVPs of Emden-Fowler type Phys. Lett. A 365 439-47
62. Horedt G P 2004 Polytropes Applications in Astrophysics and Related Fields (Dordrecht: Kluwer Academic)
63. Singh O P, Pandey R K and Singh V K 2009 An analytic algorithm of Lane-Emden type equations arising in astrophysics using modified Homotopy analysis method Comput. Phys. Commun. 180 1116-24
64. Aslanov A 2008 A generalization of the Lane-Emden equation Int. J. Comput. Math. 85 1709-25
65. Bataineh A S, Noorani M S M and Hashim I 2009 Homotopy analysis method for singular IVPs of Emden-Fowler type Commun. Nonlinear Sci. Numer. Simul. 14 1121-31
66. Yildirim A and Öziş T 2009 Solutions of singular IVPs of Lane-Emden type by the variational iteration method Nonlinear Anal. Theory Methods Appl. 70 2480-4