The use of CESTAC method to find optimal shape parameter and optimal number of points in RBF-meshless methods to solve differential equations

Document Type : Research Paper


Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.


One of the schemes to find the optimal shape parameter and optimal number of points in the radial basis function (RBF) methods is to apply the stochastic arithmetic (SA) in place of the common floating-point arithmetic (FPA). The main purpose of this work is to introduce a reliable approach based on this new arithmetic to compute the local optimal shape parameter and number of points in multiquadric and Gaussian RBF-meshless methods for solving differential equations, in the iterative process. To this end, the CESTAC method is applied. Also, in order to implement the proposed algorithms, the CADNA library is performed. The examples illustrate the efficiency and importance of using this library to validate the results.


Volume 8, Issue 4
November 2020
Pages 685-707
  • Receive Date: 09 June 2018
  • Revise Date: 02 November 2018
  • Accept Date: 16 June 2019
  • First Publish Date: 01 November 2020