Numerical Investigation of Nonlinear Parabolic Dynamical Wave Equations Using Modified Variational Iteration Algorithm-II - Mohammed, Sizar Abid; Ali, Nawzad Hasan (Politeknik Negeri Batam, 2026)
In this study, the Modified Variational Iteration Algorithm-II (MVIA-II) is implemented as a robust numerical scheme for solving nonlinear Parabolic partial differential equations. The study focuses on the implementation of an auxiliary parameter h into the correction functional to control the convergence region of the approximate series solution. To validate the efficiency of this semi-numerical approach, two fundamental models arising in mathematical physics and biology are investigated: The Allen-Cahn equation and the Newell-Whitehead equation. The results are compared with exact analytical solutions and other existing numerical methods. The error analysis demonstrates that the proposed algorithm yields high accuracy with minimal computational overhead, making it a promising tool for simulating nonlinear dynamical wave phenomena.