Solving Obstacle Problems using Optimal Homotopy Asymptotic Method

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.