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Convergence Studies for Separate Node Ascending Derivatives Expansion (SNADE) on Complex Plane
Derya Bodur, Metin Demiralp

Last modified: 2020-01-28


In this work we focus on the method called “Separate Node Ascending Derivatives Expansion (SNADE)” which is obtained as a re-sult of the studies recently carried out in Group for Science and Methods of Computing (G4S&MC) under the leadership of Metin Demiralp.SNADE is considered as a new Taylor Series Expansion. This method isrevealed as generalization of the Taylor Series Expansion and is used as an approximation to univariate functions. SNADE differs from the Taylor method by using different nodal values in each derivatives of a function. We will focus on the transition from real-valuedness to complex-valuedness and SNADE’s convergence investigations will be carried out on the complex plane. Here, “Perturbation Theory” will beused to determine the convergence region. First, boundaries for SNADE polynomials and then, boundaries for derivations of the target functionswill be obtained; and finally, disk of convergence of SNADE will be determined with these findings.