International Journal of Electrical and Computer Engineering (IJECE) Vol. 13, No. 2, April 2023, pp. 2131~2141 ISSN: 2088-8708, DOI: 10.11591/ijece.v13i2.pp2131-2141  2131 Journal homepage: http://ijece.iaescore.com Implementation of variational iteration method for various types of linear and nonlinear partial differential equations Muhammad A. Shihab 1 , Wafaa M. Taha 2 , Raad A. Hameed 1 , Ali Jameel 3,4 , Ibrahim Mohammed Sulaiman 4 1 Mathematics Department, College of Education for Pure Sciences, University of Tikrit, Tikrit, Iraq 2 Mathematics Department, College of Sciences, University of Kirkuk, Kirkuk, Iraq 3 Faculty of Education and Arts, Sohar University, Sohar, Oman 4 Institute of Strategic Industrial Decision Modelling, School of Quantitative Sciences, Universiti Utara Malaysia, Sintok, Malaysia Article Info ABSTRACT Article history: Received Mar 16, 2022 Revised Sep 24, 2022 Accepted Oct 20, 2022 There are various linear and nonlinear one-dimensional partial differential equations that are the focus of this research. There are a large number of these equations that cannot be solved analytically or precisely. The evaluation of nonlinear partial differential equations, even if analytical solutions exist, may be problematic. Therefore, it may be necessary to use approximate analytical methodologies to solve these issues. As a result, a more effective and accurate approach must be investigated and analyzed. It is shown in this study that the Lagrange multiplier may be used to get an ideal value for parameters in a functional form and then used to construct an iterative series solution. Linear and nonlinear partial differential equations may both be solved using the variational iteration method (VIM) method, thanks to its high computing power and high efficiency. Decoding and analyzing possible Korteweg-De-Vries, Benjamin, and Airy equations demonstrates the method’s ability. With just a few iterations, the produced findings are very effective, precise, and convergent to the exact answer. As a result, solving nonlinear equations using VIM is regarded as a viable option. Keywords: Airy equation Benjamin equation Lagrange multiplier Partial differential equations Potential Korteweg-De-Vries Variational iteration method This is an open access article under the CC BY-SA license. Corresponding Author: Ali Jameel Faculty of Education and Arts, Sohar University Sohar 3111, Oman Email: AJassar@su.edu.om 1. INTRODUCTION There are numerous fields of science and engineering where nonlinear phenomena are fundamental. There are numerous fields of science and engineering where nonlinear phenomena are of fundamental importance, and this is no exception. Neither numerically nor analytically, it is still difficult to solve the nonlinear models of real-world problems [1]. The study of partial differential equations began in the eighteenth-century AD with a group of researchers such as Dalembert, Euler, and Lagrange such as issues related to heat, sound, elasticity, and fluid flow. Linear and nonlinear partial differential equations (PDE) are significant in many domains, including science and engineering, chemical reaction, fluid dynamics, nonlinear optics, dispersion, and plasma physics. Not all PDE problems in real-world models can be simply solved using differential equations. As a result, rather than solving those PDEs analytically, the optimal result can be obtained numerically or approximately. Also, we seek to obtain more accurate solutions for these problems which have great effectiveness in real life systems, such as the Adomian decomposition method (ADM) [2], [3], differential transform method (DTM) [4]–[6], homotropy perturbation method (HPM) [7]–[9], the local meshless method (LMM) [10]–[15], variational iteration method (VIM) [16], [17], the fractional iterative