Solving Different Order Boundary Value Problems by Applying Homotopy Type Methods
Muhammad Naeem
Department of Basic Sciences, CECOS University of IT and Emerging Sciences, Peshawar, Pakistan
Zahid Khan
Department of Mathematics, Peshawar Model Degree College Hayatabad, Peshawar, 25000, KP, Pakistan
Sher Muhammad *
Department of Basic Sciences, CECOS University of IT and Emerging Sciences, Peshawar, Pakistan and Department of Mathematics, Islamia College, Peshawar, 25000, KP, Pakistan
Liaqat Khan
Department of Mathematics, Islamia College, Peshawar, 25000, KP, Pakistan and Department of Mathematics, Malala Yousafzai Danish School Jand, Attock, 43100, Pakistan
Jamal Uddin
Department of Physical and Numerical Sciences, Qurtuba University of Science and IT, Peshawar 25000, KP, Pakistan
*Author to whom correspondence should be addressed.
Abstract
In this manuscript, the methods, Optimal Homotopy Asymptotic Method (OHAM), Homotopy Perturbation Method (HPM) and Homotopy Analysis Method (HAM) are applied to solve various order boundary value problems. These techniques give solutions in the form of a series. Their solutions and graphs are compared with their exact solutions and graphs. All these give profitable results, but the Optimal Homotopy Asymptotic Method is more precise, whose convergence is restrained optimizations and the convergence area can be accustomed affording to the problem concerned. The results show that the suggested scheme is more active and relaxed to routine.
Keywords: OHAM, HPM, HAM, various order boundary value problems