This study uses the Variational Iteration Method (VIM) and hybrid VIM methods such as Variational Iteration Adomian Decomposition Method (VIADM), New Modified Kamal Variational Iteration Adomian Decomposition Method (NMKVIADM) to investigate the Analytical Approximate Solutions of Non Linear Partial Differential Equations such as Non Linear Wave Equations, In viscid and Viscid Burgers’ Equations, etc. Laplace Variational Iteration Method (LVIM), Modified Variational Iteration Laplace Transform Method (MVILTM), and others. VIM is a powerful tool for solving differential equations that produces quick consecutive approximations without the use of conditional assumptions or additional transformations that could alter the physical behaviour of the problem. The Adomian Decomposition method is also a useful tool for solving linear and nonlinear differential and integral equations with initial and boundary conditions. Situations. It provides an iteratively obtained effective numerical solution in the form of an infinite sequence. Using Adomian polynomials, it normally converges to the exact solution. To solve linear initial value problems, the Laplace Transform is a common and efficient integral transform. The Kamal Transform is a relatively new integral transform for solving linear initial value problems. To solve the equations, a variety of methods was used, and it was attempted to be implemented in order to solve the Non Linear Partial Differential Equations. The aim of this study is to see how hybrid VIM methods affect and how accurate they are. We compared the solutions with various approaches to demonstrate the efficiency of the methods. The obtained results show that this alternative method converges quickly, assists in obtaining precision, and manages discontinuities.
Author (s) Details
Ms. Shruti S. Sheth
Sarvajanik College of Engineering & Technology, Dr. R. K. Desai Marg, Opp. Mission Hospital, Athwalines, Suart-395001, Gujarat, India.
Dr. Twinkle R. Singh
Sardar Vallabhbhai National Institute of Technology, Ichchanath, Surat-Dumas Road, Suart-395007, Gujarat, India.
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