Convergence Characteristics of Variational Iteration Method on Ordinary Differential Equations: Theory and Applications

Abstract

Due to its inherent flexibility and accuracy in solving equations, the Variational Iteration Method (VIM) has proven to be a potent technique for addressing both linear and nonlinear models. In this work, a different method for solving VIM is presented, and its convergence to differential equations is examined. The main goals are to give error estimates and sufficient conditions for convergence. VIM is applied to ordinary differential equations in simplified forms, and convergence results and efficiency are discussed. The convergence features of VIM are investigated through in-depth study, revealing underlying mechanisms and illuminating its iterative nature. This study advances our knowledge of the theoretical underpinnings and practical applications of VIM in ordinary differential equations, improving its dependability and suitability for use in real-world problem-solving situations. Our findings enhance understanding of VIM's iterative nature, advance theoretical knowledge, and suggest avenues for future applications and improvements.These observations about the convergence of VIM confirmed the reliability of VIMfor solving real-world problems, advancing its applicability in computational science and engineering.