10.57647/ijm2c.2026.1603.17

Application of lRBF-FD Method for Numerical Solution of the Obstacle Problem

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  • Ahmed Awad Nasser1,
  • Masoud Allame*1,
  • Habeeb Abed Kadhim Aal-Rkhais2,
  • Majid Tavassoli Kajani1,
  1. Department of Mathematics, Isf. C., Islamic Azad University, Isfahan
  2. Department of Mathematics, College of Computer and Mathematics, Uinversity of Thi-Qar, Iraq

Received: 03-11-2025

Revised: 13-12-2025

Accepted: 16-12-2025

Published in Issue 30-09-2026

Published Online: 27-12-2025

Copyright (c) 2025 Ahmed Awad Nasser, Masoud Allame, Habeeb Abed Kadhim Aal-Rkhais, Majid Tavassoli Kajani (Author)

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Awad Nasser, A., Allame, M., Abed Kadhim Aal-Rkhais, H., & Tavassoli Kajani, M. (2026). Application of lRBF-FD Method for Numerical Solution of the Obstacle Problem. International Journal of Mathematical Modelling & Computations, 16(3), 217-223. https://doi.org/10.57647/ijm2c.2026.1603.17
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Abstract

The obstacle problem is a nonlinear variational inequality, first introduced to model contact phenomena in solid mechanics. Because of the singularity of the solution along the free boundary, the development of accurate and efficient numerical methods is critical. This paper introduces a novel meshless technique for numerically solving the obstacle problem, utilizing the local radial basis function-finite difference (lRBF-FD) method. An active set strategy is combined with the lRBF-FD method to manage the complementarity condition of the problem. Notable advantages of this method are its independence from any mesh and its straightforward implementation with high numerical stability. 

Keywords

  • Obstacle problem,
  • Active set method,
  • Radial basis functions,
  • Meshfree method,
  • Finite difference method
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