Separate Node Ascending Derivatives Expansion (SNADE) as a Univariate Function Representation

Keywords: SNADE, Integral Operator, Taylor Series, Multinode Expansion, Cauchy Contour Integral REFERENCES [1] M. Demiralp Separate Node Ascending Derivatives Expansion (SNADE) for Univariate Functions: Conceptuality and Formulation AIP Proceedings for the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2014), 22-28 September 2014, Rhodes, Greece, 2014, Vol 9, pp. 146-159. [1] M. Demiralp Separate Node Ascending Derivatives Expansion (SNADE) for Univariate Functions: Conceptuality and Formulation AIP Proceedings for the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2014), 22-28 September 2014, Rhodes, Greece, 2014, Vol 9, pp. 146-159. [2] N.A. Baykara, and M. Demiralp, Separate Node Ascending Derivatives Expansion (SNADE) for Univariate Functions: Polynomial Recursions, Remainder Bounds and the Convergence AIP Proceedings for the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2014), 22-28 September 2014, Rhodes, Greece, 2014, Vol 1, pp. 407-414. [3] N.A. Baykara, and E. Gurvit, ¨ Separate Node Ascending Derivatives Expansion (SNADE) for Univariate Functions: Univariate Numerical Integration, AIP Proceedings for the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2014), 22-28 September 2014, Rhodes, Greece (in print), 2014. [4] E. Gurvit, and N.A. Baykara, ¨ Separate Node Ascending Derivatives Expansion (SNADE) for Univariate Functions: Node Optimization via Partial Fluctuation Suppression, AIP Proceedings for the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2014), 22-28 September 2014, Rhodes, Greece (in print), 2014. [5] B. Tunga, Separate multinode ascending derivatives expansion (Demiralps SMADE): Basis polynomial, 11th International Conference of Computational Methods in Sciences and Engineering, ICCMSE 2015, 20-23 Mart 2015, Athens, Greece (in print). [6] D. Bodur, and M. Demiralp, 2 Very Specific Cases for Separate Node Ascending Derivatives Expansion (SNADE), 11th International Conference of Computational Methods in Sciences and Engineering, ICCMSE 2015, 20-23 Mart 2015, Athens, Greece (in print). [7] G. Thomas, and L.R. Finney, Calculus and Analytic Geometry (9th ed.), Addison Wesley, ISBN 0-201-53174-7, 1996. [8] M. Demiralp, Convergence issues in the gaussian weighted multidimensional fluctuation expansion for the univariate numerical integration, WSEAS Transactions on Mathematics, 4:486-492, 2005. [9] C. Goz¨ ukırmızı, and M. Demiralp, ¨ The application of the fluctuation expansion with extended basis set to numerical integration, WSEAS Transactions on Mathematics, 8(5):205-212, 2009 [10] E. Gurvit, N.A. Baykara, and M. Demiralp, ¨ Numerical integration of bivariate functions over a nonrectangular area by using fluctuationlessness theorem, WSEAS Transactions on Mathematics, 8(5):193-198, 2009. [11] N.A. Baykara, E. Gurvit, and M. Demiralp, ¨ The fluctuationlessness approach to the numerical integration of functions with a single variable by integrating taylor expansion with explicit remainder term, J. Math. Chem., 49(2):393-406, 2011. [12] N.A. Baykara, E. Gurvit, and M. Demiralp, ¨ Fluctuationless univariate integration through taylor expansion with remainder by using oscillatory function basis sets, In AIP Proceedings for the International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2009), volume 1168, pages 428-431, Rethymno, Crete, Greece, 18-22 September 2009.