Solving Obstacle Problems using Optimal Homotopy Asymptotic Method (Global Journal of Sciences, 2025)
Differential equations play a vital role in explaining real-world phenomena  across science and engineering, from fluid motion and population growth to the  mechanics of bridges. In particular, the cantilever bridge problem can be  framed as a homogeneous obstacle problem, which illustrates the practical  importance of such mathematical models. Although obstacle problems have  been studied extensively, many existing approaches leave gaps that limit their  effectiveness. In this work, we apply the Optimal Homotopy Asymptotic  Method (OHAM) to derive exact solutions for several obstacle problems. Our  findings not only demonstrate the accuracy and efficiency of this approach but  also highlight interesting structural symmetries, as revealed through graphical  results that provide deeper insight into the nature of these problems.
Keywords: Obstacle problems; Optimal homotopy; asymptotic method; Numerical problems