Charlier Series Solutions of Systems of First Order Delay Differential Equations with Proportional and Constant Arguments

This study is devoted to obtaining the Charlier series solutions of first order delay differential equations involving proportional and constant arguments by employing an inventive numerical method dependent upon a collaboration of matrix structures derived from the parametric Charlier polynomial. The method essentially conducts the conversion of the unknown terms into a unique matrix equation at the collocation points, which yields a direct computation for these stiff equations. Two illustrative examples are included to test the accuracy and efficiency of the method. According to the investigation of the graphical and numerical results, the method holds fast, inventive and accurate computation, regularizing the matrix forms in compliance with the equations in question.