Abstract
In this paper, various homotopy approaches such as Homotopy
Perturbation Method (HPM) and Optimal Homotopy Asymptotic Method
(OHAM) are applied to solve the greater order multipoint boundary value
problems. The problem 4.1 is solved by OHAM and HPM and their results are compared with their exact solutions and problem 4.2 is solved by
OHAM only and its results are compared with its exact solution and Vibrational Iteration Method VIM has taken from references [29, 30] The problem 4.3 is solved by OHAM and its result is compared with its exact solution and variational iteration method homotopy perturbation (VIMHP)
taken from reference [26]. The new analytical algorithm OHAM provides
us with a convenient way to control the convergence of approximation
series and allows adjustment of convergence regions where necessary. It
has a very good agreement with the exact solution of the concerned problem. It is a parameter free method and shows reliability, so that the results
reveal the effectiveness of OHAM which leads to better accuracy
Muhammad Naeem, Sher Muhammad, Syed Asif Hussain, Zaheer Ud Din, Liaqat Ali. (2019) Applying Homotopy Type Techniques to Higher Order Boundary Value Problems, Punjab University Journal of Mathematics, Volume 51, Issue 2.
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