In this paper, we have proposed a new iterative method for finding the solution of ordinary differential equations of the first order. In this method we have extended the idea of variational iteration method by changing the general Lagrange multiplier which is defined in the context of the variational iteration method.This causes the convergent rate of the method increased compared with the var...

Ordinary generating series of multiple harmonic sums admit a full singular expansion in the basis of functions {(1 − z) log(1 − z)}α∈Z,β∈N, near the singularity z = 1. A constructive proof of this result is given, and, by combinatoric aspects, an explicit evaluation of Taylor coefficients of functions in some polylogarithmic algebra is obtained. In particular, the asymptotic expansion of multip...

Improving the order of accuracy for any numerical method remains a continuing quest. For a large class of computational uid dynamics (CFD) problems, the discrete approximate solution error is viewed as truncation of a Taylor series expansion. In this paper, a weak statement Galerkin matrix perturbation (GMP) method is utilized yielding simple tridiagonal forms that reduce, or annihilate in spec...

Recently-developed variational perturbation expansions converge exponentially fast for positive coupling constants. They do not, however, possess the correct left-hand cut in the complex coupling constant plane, implying a wrong large-order behavior of their Taylor expansion coeecients. We correct this deeciency and present a method of resumming divergent series with their proper large-order be...

This paper presents a Taylor series approach for solving linear fractional de-centralized bi-level multi-objective decision-making (LFDBL-MODM) problems with asingle decision maker at the upper level and multiple decision makers at the lower level.In the proposed approach, the membership functions associated with each objective(s) ofthe level(s) of LFDBL-MODM are transformed by using a Taylor s...

An alternative parametric description for discrete random variables, called muculants, is proposed. Contrary to cumulants, muculants are based on the Fourier series expansion rather than on the Taylor series expansion of the logarithm of the characteristic function. Utilizing results from cepstral theory, elementary properties of muculants are derived. A connection between muculants and cumulan...

This work concerns the solution of generalized Riemann problems. To this end, we consider the ADER scheme of Titarev & Toro (2002), which relies on a generalization of the classical Godunov scheme. Another solution method is the power series expansion of LeFloch & Raviart (1988). We analyze the two resulting approximation schemes, where we show that for scalar 1d problems the Toro-Titarev solve...