Solving Obstacle Problems using Optimal Homotopy Asymptotic Method

TL;DR

This paper introduces the use of the optimal homotopy asymptotic method (OHAM) to find exact solutions to various obstacle problems, demonstrating its effectiveness through graphical results.

Contribution

The paper applies OHAM to obstacle problems, providing a novel approach not previously explored in the literature for these types of differential equations.

Findings

Successful application of OHAM to obstacle problems

Graphical results show symmetry and accuracy

Method offers a new solution technique for obstacle problems

Abstract

Differential equations have void applications in several practical situations, sciences, and non sciences as Euler Lagrange equation in classical mechanics, Radioactive decay in nuclear physics, Navier Stokes equations in fluid dynamics, Verhulst equation in biological population growth, Hodgkin Huxley model in neural action potentials, etc. The cantilever bridge problem is very important in Bridge Engineering and this can be modeled as a homogeneous obstacle problem in Mathematics. Due to this and various other applications, obstacle problems become an important part of our literature. A lot of work is dedicated to the solution of the obstacle problems. However, obstacle problems are not solved by the considered method in the literature we have visited. In this work, we have investigated the finding of the exact solution to several obstacle problems using the optimal homotopy asymptotic method (OHAM). The graphical representation of results represents the symmetry among them.