Study of the stability of a meshless generalized finite difference scheme applied to the wave equation

FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS(2023)

Cited 0|Views2
No score
Abstract
When designing and implementing numerical schemes, it is imperative to consider the stability of the applied methods. Prior research has presented different results for the stability of generalized finite-difference methods applied to advection and diffusion equations. In recent years, research has explored a generalized finite-difference approach to the advection-diffusion equation solved on non-rectangular and highly irregular regions using convex, logically rectangular grids. This paper presents a study on the stability of generalized finite difference schemes applied to the numerical solution of the wave equation, solved on clouds of points for highly irregular domains. The stability analysis presented in this work provides significant insights into the proper discretizations needed to obtain stable and satisfactory results. The proposed explicit scheme is conditionally stable, while the implicit scheme is unconditionally stable. Notably, the stability analyses presented in this paper apply to any scheme which is at least second order in space, not just the proposed approach. The proposed scheme offers effective means of numerically solving the wave equation, particularly for highly irregular domains. By demonstrating the stability of the scheme, this study provides a foundation for further research in this area.
More
Translated text
Key words
stability analysis,meshless method,generalized finite difference,wave equation,numerical solution of PDE
AI Read Science
Must-Reading Tree
Example
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined