Purpose <p>Machining vibrations caused by tool-workpiece interactions can deteriorate surface quality, reduce tool life, and affect dimensional accuracy. Accurate modeling of such phenomena requires mathematical formulations that incorporate memory effects and time-dependent delays related to spindle speed variations. The purpose of this study is to develop an efficient numerical method for solving delay integro-differential equations arising in machine tool vibration models.</p> Methods <p>A collocation method based on locally supported thin plate splines (TPS) is developed to approximate the solution of integro-differential equations with time-varying delay. The method employs local neighborhoods around selected nodes, resulting in several small linear systems instead of a single global system. This localized, meshless strategy significantly reduces computational cost and CPU time.</p> Results <p>Error analysis, convergence studies, and numerical simulations are presented to assess the accuracy and stability of the proposed approach. Numerical results demonstrate that the scheme achieves high accuracy and stability for solving integro-differential equations with time-dependent delays while substantially reducing computational cost compared to global methods.</p> Conclusion <p>The presented method provides an efficient and accurate tool for simulating machine tool vibrations governed by delay integro-differential equations. Its meshless nature, reduced computational demand, strong convergence properties, and applicability to two-dimensional space-time problems make it well suited for practical engineering applications and implementation on standard personal computers.</p>