Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 Articles in Press 2026 04 17 Accurate and efficient multilevel v-cycle algorithm for meshfree RBF method 6020 10.22060/ajmc.2025.24615.1443 EN Nikunja Bihari Barik PG Department of Mathematics, Government DAV College, Koraput-764021, India 0000-0002-6476-2755 Kanaka Lata Ojha Department of Mathematics, Siksha ‘O’ Anusandhan University, Bhubaneswar, Odisha, India Sekhar TVS School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar-752050, India Debasish Mishra Centurion University of Technology and Management, Odisha, India Journal Article 2025 08 23 An accurate and efficient multilevel v-cycle algorithm for radial basis function-based finite difference (RBF-FD) method is presented in this paper. The primary goal of the algorithm is level-by-level calculation from finest level to coarsest level and then level-by-level correction from coarsest level to finest level. The algorithm produces an accurate solution by solving corresponding error equations of the discretized equations from coarsest level to coarser level and then finer level to desired finest level. Convection-dominated problems are taken to demonstrate the validity of the algorithm. The computing time of the proposed algorithm is calculated, and it saves at least 51% of computation time than the general RBF-FD method. The necessary and sufficient convergence conditions of the iteration matrix of the proposed method were verified numerically. The tests show that the developed algorithm is accurate, which accelerates to a significant reduction in computational cost compared with the general RBF-FD method.