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All Journal JOURNAL OF APPLIED INFORMATICS AND COMPUTING Jurnal Diferensial
Ali, Nawzad Hasan
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Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Mathematics Public Health

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Numerical Investigation of Nonlinear Parabolic Dynamical Wave Equations Using Modified Variational Iteration Algorithm-II Mohammed, Sizar Abid; Ali, Nawzad Hasan
Journal of Applied Informatics and Computing Vol. 10 No. 1 (2026): February 2026
Publisher : Politeknik Negeri Batam

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30871/jaic.v10i1.12107

Abstract

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.
A Solutions of the Linearized Two-Dimensional Generalized Dispersive Wave Equation with Mixed Derivative via the Residual Power Series Method Ali, Nawzad Hasan
JURNAL DIFERENSIAL Vol 8 No 1 (2026): April 2026
Publisher : Program Studi Matematika, Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35508/jd.v8i1.26631

Abstract

This article applies the Residual Power Series Method (RPSM) to solve the Linearized Two-Dimensional Generalized Dispersive Wave Equation (L-2DGDWE) featuring the mixed derivative term $u_{xt}$. The RPSM is based on the general Taylor series formula combined with a residual error function minimization. A new analytical solution is investigated in this work. The analytical solution is designed to find approximate solutions via RPSM, and these obtained results are compared with exact solutions to demonstrate the precision, reliability, and rapid convergence of the proposed method. Graphical representations at different time instances are provided to visualize the solution behavior.
Co-Authors Mohammed, Sizar Abid