IJPAM: Volume 46, No. 2 (2008)

Invited Lecture Delivered at
Forth International Conference of Applied Mathematics
and Computing (Plovdiv, Bulgaria, August 12-18, 2007)


A. Golbabai$^1$, S. Seifollahi$^2$, R. Gholami$^3$
$^1$Department of Mathematics
Iran University of Science and Technology
Narmak, Tehran, 16844, IRAN
e-mail: golbabai@iust.ac.ir
$^{2,3}$Department of Mathematics
Islamic Azad University
Karaj Baranch, IRAN

Abstract.In this paper, we demonstrate the efficiency of the multiquadric radial basis functions (MQ-RBFs) collocation method for solving partial differential equations (PDEs), as theoretically compared to the finite element method (FEM). The MQ-RBF has the property of exponential convergence with respect to the shape parameter. Although the optimal choice of shape parameter is still an unsettled issue, there exist a wide range $c$ of values in which the RBF solution has high accuracy. Error estimation of the approximate solution is also given and the numerical results indicate that the method provides accurate approximations.

Received: August 17, 2007

AMS Subject Classification: 73V05, 65D05

Key Words and Phrases: radial basis function, finite element method, multivariate interpolation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 46
Issue: 2