DOI: 10.5176/2251-1911_CMCGS16.28
Authors: Suheil Khoury, Alaa Bakir and Ali Sayfy
Abstract: In this paper, we present a numerical algorithm that is based on embedding Green’s function into fixed point iteration schemes, such as Picard’s and Mann’s. This proposed strategy is implemented to solve a wide class of second and third order nonlinear boundary value problems (BVPs) that appear in various physical aspects. A convergence theorem is also given. After describing the approach, we apply it to two numerical examples whose analytical solutions are known. A comparison between the numerical and the exact solutions determines and confirms the high accuracy, efficiency and fast convergence of our method.
Keywords: Green’s function; fixed point iteration schemes; nonlinear boundary value problems
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