A Novel Computational Framework for Nonlinear Differential Equations Employing the Modified Laplace Adomian Polynomial Method - Salisu Lukunti; Umar Mujahid Aliyu; Abubakar Assidiq Hussaini; Imafidor Hassan Ibrahim; Mohammed Abubakar Kolo; Sulaiman Ahmad; Nura Hashim; Mohammed Yusuf Marafa (Darul Yasin Al Sys, 2026)
Nonlinear differential equations arise widely in applied mathematics, physics, and engineering, yet many conventional analytical and numerical methods remain limited in their ability to handle strong nonlinearities efficiently and accurately. This paper presents a novel computational framework based on the Modified Laplace–Adomian Polynomial Method (LAPM) for solving nonlinear differential equations. The proposed method integrates the Laplace transform with an enhanced form of the Adomian Decomposition Method, enabling complex nonlinear terms to be decomposed into rapidly convergent Adomian polynomials. This integration simplifies the solution procedure, reduces computational complexity, and preserves high accuracy. The performance of LAPM was validated using several benchmark nonlinear and linear differential equations, and the results demonstrated superior convergence speed, precision, and stability compared with traditional methods. The study concludes that the Modified Laplace–Adomian Polynomial Method is a reliable and efficient approach for solving a broad class of nonlinear differential equations. This work contributes to the advancement of computational methods by offering a robust alternative for the analysis of differential equation models encountered in mathematics, physics, and engineering.