Recent Study on the Computation of the Lagrange Multiplier for the Variational Iteration Method (VIM) for Solving Differential Equations | Chapter 1 | Theory and Practice of Mathematics and Computer Science Vol. 9

 The Variational Iteration Method (VIM) is used to find the solution of differential equations in this chapter, with a focus on the option of the Lagrange multiplier when using VIM. Only the non-linear term in the correction functional is subjected to restricted variation. The operator D-Method and integrating factor are used in some aspects of determining the exact Lagrange multiplier for VIM, based on current methods and variational theories. When the computed exact Lagrange multiplier was compared to the approximate Lagrange multiplier, it was found that the computed exact Lagrange multiplier decreased the number of iterations needed to get a good approximate result by a large amount, and in some cases, the result converged to the exact solution after just one iteration. MAPLE Software is used to conduct the evaluations.

Author (s) Details

N. Okiotor
Department of Mathematics, University of Abuja, Abuja, Nigeria.

Prof. F. Ogunfiditimi
Department of Mathematics, University of Abuja, Abuja, Nigeria.

View Book :- https://stm.bookpi.org/TPMCS-V9/article/view/848

Applications on Hybrid VIM Methods | Chapter 7 | New Insights into Physical Science Vol. 13

 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.

View Book :- https://stm.bookpi.org/NIPS-V13/issue/view/51