We develop a high accuracy power series method for solving partial differential equations with emphasis on the nonlinear Schrödinger equations. The and computing speed can be systematically arbitrarily increased to orders of magnitude larger than those other methods. Machine precision easily reached sustained long evolution times within rather short time. In-depth analysis characterisation all ...

A general optimization method, based on the power series is presented for computing conformal mappings with explicit expressions from: (a) unit disc onto an infinite domain exterior of a closed Jordan curve, (b) circular annulus finite doubly-connected bounded by two curves, (c) curves non-circular curves. The unknown mapping functions are approximated method. problem solving function coefficie...

This paper presents a method for prediction short-term power demand of a vehicular power system. The forecasting of power demand is presented using wavelet decomposition and artificial neural network, a hybrid model which absorbs some merits of wavelet transform and neural network. The power demand time series is first decomposed into a certain number of levels with discreet wavelet transform a...

Many results which are obtained or unable to by classical calculus have also been studied q-calculus. It is effective use q-calculus since it acts as a bridge between mathematics and physics. The q-analog of Chlodowsky operators has introduced the approximation properties these in [12]. Then [23], Stancu-Chlodowsky some via A-statistical convergence more general setting.In this paper, we presen...

In this research, systems of linear and nonlinear differential equations fractional order are solved analytically using the novel interesting method: ARA- Residual Power Series (ARA-RPS) technique. This approach technique is based on combination residual power series scheme with ARA transform to establish analytical approximate solutions in a fast convergent representation concept limit. The pr...

The aim of this paper is to give different inequalities which result from various generalizations of Young inequalities in some specific cases for a and b using the power series method used by C. Mortici in his paper, [10]. Also several integral forms for some inequalities deduced by power series method starting from certain inequalities which generalize Radon’s inequality will be presented. Ma...

The computational method based on using the operational matrix of anorthogonal function for solving variational problems is computeroriented. In this approach, a truncated Hartley series together withthe operational matrix of integration and integration of the crossproduct of two cas vectors are used for finding the solution ofvariational problems. Two illustrative...

In this paper, free vibration analysis and forced vibration analysis of FG doubly clamped micro-beams is studied based on the third order shear deformation and modified couple stress theories. The size dependent dynamic equilibrium equations and both the classical and non-classical boundary conditions are derived using a variational approach. It is assumed that all properties of the FG micro-be...