Novel dual method approach for solving third order pseudo hyperbolic PDEs using variational iteration and group preserving schemes

Abstract

The study explores advanced numerical techniques for solving pseudo-hyperbolic equations through an innovative computational approach integrating variational iteration methodology, symmetry-preserving numerical schemes, and a novel fictitious time discretization strategy. By transforming the original mathematical problem into an alternative formulation using fictitious time integration, we develop a robust computational framework that enhances numerical stability and convergence properties. The proposed method leverages group-preserving transformation techniques to maintain critical mathematical symmetries throughout the numerical solution process. Comprehensive numerical experiments are conducted across diverse test scenarios to validate the method's performance and computational efficiency. Rigorous analysis demonstrates the approach's significant advantages, including rapid convergence, high accuracy, and exceptional adaptability to complex pseudo-hyperbolic systems. The research contributes novel insights into advanced computational mathematics, offering a sophisticated alternative to traditional numerical solution strategies for challenging partial differential equations. Detailed numerical simulations substantiate the method's effectiveness, revealing its potential for addressing intricate mathematical modeling challenges in various scientific and engineering domains.