OICC Press International Journal of Mathematical Modelling & Computations 2228-6233 16 3 2026 09 30 Application of lRBF-FD Method for Numerical Solution of the Obstacle Problem 217 223 10.57647/ijm2c.2026.1603.17 EN Ahmed Awad Nasser Department of Mathematics, Isf. C., Islamic Azad University, Isfahan Masoud Allame Department of Mathematics, Isf. C., Islamic Azad University, Isfahan Habeeb Abed Kadhim Aal-Rkhais Department of Mathematics, College of Computer and Mathematics, Uinversity of Thi-Qar, Iraq https://orcid.org/0000-0001-5692-2993 Majid Tavassoli Kajani Department of Mathematics, Isf. C., Islamic Azad University, Isfahan https://orcid.org/0000-0003-3592-1304 Journal Article 2026 09 30 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.