Hermite Wavelet Operational Matrix Method for Solving Neutral Coupled Delay Differential Equations With Multiple Delays

Neutral delay differential equations (NDDEs) are established in various applications, such as signal processing, control systems, epidemiology, and dynamical systems. In this research work, we introduce the Hermite wavelet operational matrix (HWOM) method of derivatives to approximate the solutions of NDDEs and systems of pantograph equations. HWOM is a computational algorithm to convert the NDDEs and the system of pantograph equations into an algebraic system with the help of sparse types of matrices. This is demonstrated through several illustrative examples. Furthermore, the obtained HWOM results are compared with exact and other numerical solutions. The efficiency of the proposed method is analyzed through the convergence and error analysis. Satisfactory agreement with the proposed method in terms of improving performance, accuracy, and robustness, and reducing computational cost.