Journals Information
Mathematics and Statistics Vol. 13(4), pp. 208 - 217
DOI: 10.13189/ms.2025.130404
Reprint (PDF) (640Kb)
Investigating the Laplace Variational Iteration Method for Solving Nonlinear Differential Equations Arising in Digital Systems
Dahiru Abdurrahman 1, Maheshwar Pathak 1,*, Pratibha Joshi 2
1 Department of Mathematics, Sharda University, Greater Noida - 201310, Uttar Pradesh, India
2 Department of Mathematics, AIAS, Amity University, Noida - 201313, Uttar Pradesh, India
ABSTRACT
The Laplace Variational Iteration Method (LVIM) discussed in this study is a powerful hybrid analytical approach that combines the strengths of the Variational Iteration Method (VIM) with the Laplace transform. Nonlinear differential equations arise frequently in modelling real-world situations across variety of fields in digital signal processing, control systems, and electronic circuit analysis where finding accurate and efficient solutions is crucial for analyzing system dynamics, ensuring stability, and optimizing performance. Traditional methods often are unable to evaluate exact or near-exact solutions for these nonlinear systems, particularly when the initial or boundary conditions are complex. The main objective of this research is to utilize LVIM to tackle specific nonlinear differential equations that are commonly encountered in digital systems. By incorporating the Laplace transform into the variational iteration methodology, this method streamlines the solution process and boosts convergence. The results are showcased through a mix of graphical plots and tables, highlighting the accuracy, computational efficiency, and robustness of the considered approach. The results show that LVIM offers a dependable and straightforward way to manage nonlinearities without involving complex techniques as linearization or perturbation techniques. While the method shows impressive performance, it is important to note that its effectiveness can hinge on the smoothness of the initial functions and the availability of Laplace transforms. This work adds to the expanding field of semi-analytical methods and provides practical insights for engineers and applied mathematicians engaged in cutting-edge digital technologies.
KEYWORDS
Differential Equations, Computational Mathematics, Digital Systems
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Dahiru Abdurrahman , Maheshwar Pathak , Pratibha Joshi , "Investigating the Laplace Variational Iteration Method for Solving Nonlinear Differential Equations Arising in Digital Systems," Mathematics and Statistics, Vol. 13, No. 4, pp. 208 - 217, 2025. DOI: 10.13189/ms.2025.130404.
(b). APA Format:
Dahiru Abdurrahman , Maheshwar Pathak , Pratibha Joshi (2025). Investigating the Laplace Variational Iteration Method for Solving Nonlinear Differential Equations Arising in Digital Systems. Mathematics and Statistics, 13(4), 208 - 217. DOI: 10.13189/ms.2025.130404.