Solving Obstacle Problems using Optimal Homotopy Asymptotic Method

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.