Semianalytical Approach for the Approximate Solution of Delay Differential Equations

• Main Authors: Habib, M. (Author), Karim, S. (Author), Luo, X. (Author), Wahash, H.A (Author)
• Format: Article
• Language: English
• Published: Hindawi Limited 2022
• Subjects: Approximate solution; Computation theory; Convolution; Convolution theorems; Delay differential equations; Differential equations; Homotopies; Homotopy perturbation transform methods; Iterative methods; Lagrange multipliers; Laplace transforms; New approaches; Perturbation method; Perturbation techniques; Semi-analytical approaches; Semi-analytical solution; Variational iteration method
• Online Access: View Fulltext in Publisher

 In this analysis, we develop a new approach to investigate the semianalytical solution of the delay differential equations. Mohand transform coupled with the homotopy perturbation method is called Mohand homotopy perturbation transform method (MHPTM) and performs the solution results in the form of series. The beauty of this approach is that it does not need to compute the values of the Lagrange multiplier as in the variational iteration method, and also, there is no need to implement the convolution theorem as in the Laplace transform. The main purpose of this scheme is to reduce the less computational work and the error analysis of the problems than others studied in the literature. Some illustrated examples are interpreted to confirm the accuracy of the newly developed scheme. © 2022 Xiankang Luo et al.