A study of obstacle problems using homotopy perturbation method

Numerical methods for solving differential equations has become an important topic of this era. The importance of boundary value problems in applied sciences shows the way in which existence of exact solution is not always possible. This study adopts the homotopy perturbation method (HPM) to solve multiple-point boundary value problems arising in obstacle, unilateral and contact problems. Convergent approximate solutions are constructed such that the exact boundary conditions are satisfied. Some examples have been presented to elucidate the efficiency and implementation of the method. We have compared the results using different number of terms of HPM and found that increasing the number of terms of approximate solution will increase the efficiency.