Exploration of novel analytical solutions of boundary layer equation via the modified sumudu transform

Abstract

The research introduces the Modified Sumudu Decomposition Method (MSDM) as a novel approach for solving non-linear ordinary differential equations. Stemming from the Sumudu Transformation (ST), proposed by Watugala in the 1990s, MSDM demonstrates its efficacy through the solution of a specific third-order non-homogeneous nonlinear ordinary differential equation. This method is particularly highlighted for its application in fluid mechanics, specifically addressing a boundary layer problem. Furthermore, the study employs Pade´ Approximants to evaluate a crucial parameter, ρ=φ''(0), and compares the results with other established methods, including Modified Laplace Decomposition Method (MLDM), Modified Adomian Decomposition Method (MADM), Modified Variational Iteration Method (MVIM), and the Homotopy Perturbation Method (HPM). The findings not only contribute to the advancement of mathematical techniques for solving complex differential equations but also provide a comparative analysis, elucidating the strengths and limitations of different methodologies. This research is anticipated to have significant implications for researchers and practitioners in the field, offering a valuable toolkit for tackling a wide range of mathematical modeling challenges.