Dejdumrong Collocation Approach and Operational Matrix for a Class of Second-Order Delay IVPs: Error Analysis and Applications

Abstract

In this paper, a collocation method based on the Dejdumrong polynomial matrix approach was used to estimate the solution of higher-order pantograph-type linear functional differential equations. The equations are considered with hybrid proportional and variable delays. The proposed method transforms the functionaltype differential equations into matrix form. The matrices were converted into a system of algebraic equations containing the Dejdumrong polynomial. The coefficients of the Dejdumrong polynomial were obtained by solving the system of algebraic equations. Moreover, the error analysis is performed, and the residual improvement technique is presented. The presented methods are applied to three examples. Finally, the obtained results are compared with the results of other methods in the literature and were found to be better compared. All results in this study have been calculated using Matlab R2021a.