Search    
IP Address: 38.103.63.*      
Login
Individual Subscriber Registration
Login Forgot Password?
 
Author Login
Author Registration
Login Forgot Password?

  Far East Journal of Applied Mathematics  
 ISSN: 0972-0960
 
 
 

     Far East Journal of Applied Mathematics
    Volume 32, Issue 1, Pages 113 - 126 (July 2008)


NUMERICAL SOLUTION OF ELLIPTIC PDEs USING RADIAL BASIS FUNCTION NETWORKS AND COMPARISON BETWEEN RBFN AND ADOMIAN METHOD

M. M. Mazarei (Iran) and A. Aminataei (Iran)

Received February 20, 2008

References:



[1] G. Adomian, Solving Frontier Problems of Physics, The Decomposition Method, Kluwer, Boston, 1994.

[2] A. Aminataei and S. S. Hosseini, Comparison of Adomian decomposition and double decomposition methods for boundary-value problems, Euro. J. Sci. Res. 2(2) (2005), 48-56.

[3] A. Aminataei and S. S. Hosseini, The comparison of the stability of Adomian decomposition method with numerical methods of equation solution, Appl. Maths. and Comput. 186 (2007), 665-669.

[4] A. Aminataei and M. Sharan, Using multiquadric method in the numerical solution of ODEs with a singularity point and PDEs in one and two dimensions, Euro. J. Sci. Res. 10(2) (2005), 19-45.

[5] R. E. Carlson and T. A. Foley, The parameter in multiquadric interpolation, Computers Math. Applic. 21 (1991), 29-42.

[6] R. Franke, Scattered data interpolation: test of some methods, Math. Comp. 38 (1982), 181-200.

[7] R. L. Hardy, Theory and applications of the multiquadric-biharmonic method, Computers Math. Applic. 19 (1990), 163-208.

[8] E. J. Kansa, Multiquadrics—a scattered data approximation scheme with applications to computational fluid dynamics-I, surface approximations and partial derivative estimates, Computers Math. Applic. 19 (8/9) (1990), 127-145.

[9] N. Mai-Duy and T. Tran-Cong, Numerical solution of differential equations using multiquadric radial basis function networks, Neural Networks 14 (2001), 185-199.

[10] G. J. Moridis and E. J. Kansa, The Laplace transform multiquadrics method: a highly accurate scheme for the numerical solution of linear partial differential equations, J. Appl. Sci. and Comput. 1(2) (1994), 375-407.

[11] A. E. Tarwater, A parameter study of Hardy’s multiquadric method for scattered interpolation, Technical Report UCRL-563670, Lawrence Livemore National Laboratory, 1985.

[12] A. M. Wazwaz, A reliable algorithm for obtaining positive solutions for nonlinear boundary-value problems, Appl. Maths. and Comput. (2001), 1237-1244.

[13] M. Zerroukat, H. Power and C. S. Chen, A numerical method for heat transfer problems using collocation and radial basis functions, Int. J. Numer. Methods Engg. 42 (1998), 1263-1278.

Keywords and phrases: radial basis function networks, multiquadric approximation scheme, solution of differential equations, boundary conditions, width of radial basis function.

 


Previous Article    Next Article

 
         

© Copy Right  PUSHPA PUBLISHING HOUSE, Vijaya Niwas, 198, Mumfordganj, Allahabad-211002, India