A Meshless Method for Numerical Solutions of Non-Homogeneous Differential Equation with Variable Delays

This paper is devoted to solve a class of differential equation with simultaneously combining variable coeffcients and variable delays namely variable-delay dierential equations (VDDEs). For this purpose, a numerical method is proposed in which the unknown function and its derivative are approximated with the basis of interpolating Multiquadric radial basis functions (MQRBFs) at arbitrary collocation points. According to the existing mechanism, the synchronization problem is recast to a system of algebraic equations. In the other hand, the proposed method provides a very adjustable framework for approximation according to the discretization and due to a board range of arbitrary nodes. Finally, some illustrative examples are given to verify the validity and applicability of the new technique and also a comparison betweenour results and the existing studies is performed.