New collocation path-following approach for the optimal shape parameter using Kernel method

Abstract The goal of this work is to develop a numerical method combining Radial Basic Functions (RBF) kernel and high order algorithm based on Taylor series homotopy continuation method. local RBF approximation applied in strong form allows us overcome the difficulties integration treat problems large deformations. Furthermore, enables transform nonlinear problem set linear problems. Determining optimal value shape parameter still an outstanding research topic. This depends density distribution points considered for e.g. boundary problems, integral equations, delay-differential equations etc. These have been extensively attempts literature which end up choosing by tests error or some other ad-hoc means. Our contribution paper suggest new strategy using radial basis functions with automatic reasonable choice case accuracy stability results. computational experiments tested examples structural analysis are performed comparison respect state art algorithms from given.