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On Multi-Quadric Based RBF–FD Method for Second-Order Diffusion Filters

Authors
  • Jetta, Mahipal1
  • Chirala, Satyanarayana1
  • 1 Mahindra École Centrale, Hyderabad, India , Hyderabad (India)
Type
Published Article
Journal
SN Computer Science
Publisher
Springer Singapore
Publication Date
Oct 23, 2019
Volume
1
Issue
1
Identifiers
DOI: 10.1007/s42979-019-0046-4
Source
Springer Nature
Keywords
License
Yellow

Abstract

The usual three-node approximations for the first-order spatial derivatives in the radial basis functions-based finite difference (RBF-FD) scheme allows relatively smaller time step size than the standard scheme (forward difference in time and central difference in space) in obtaining stable results. In this paper, to better mimic the continuous model, we use nine nodal points in RBF–FD approximation of first-order spatial derivatives. We then employ these approximations to solve a two-dimensional nonlinear diffusion equation from image processing. The constructed numerical scheme is shown to be stable and allows up to obtain four times bigger time step size than the standard scheme.

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