Extended Abstract. Forecasting is one of the most important purposes of time series analysis. For many years, classical methods were used for this aim. But these methods do not give good performance results for real time series due to non-linearity and non-stationarity of these data sets. On one hand, most of real world time series data display a time-varying second order structure. On th...

Structural damage can be identified by processing structural vibration response signals and excitation data, and thus the suitability of signal processing methods is essential to structural damage identification. To explore an intelligent signal processing method for structural damage identification, the paper integrated wavelet real-time filtering algorithm, Adaptive Neruo-Fuzzy Inference Syst...

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe the propagation of local errors in this method, and show that the global order of RK5GL3 is expected to be six, one better than the underlying RungeKutta m...

In this study, an efficient semi-discrete method based on the two-dimensional Legendre wavelets (2D LWs) is developed to provide approximate solutions for nonlinear variable-order time fractional (2D) Schrödinger equation. First, derivative involved in considered problem approximated via finite difference technique. Then, by help of scheme and theta-weighted method,...

geophysical data are always affected by different sources of anomaly. these sources are classified in to three groups: first group is relatively deep sources commonly called as regional effects, second group is near surface sources or local effects and third group is high frequency noises. the only common way to separate the anomaly is separation with respect to the signal frequency. there are ...

This paper gives an efficient numerical method for solving the nonlinear system of Volterra-Fredholm integral equations. A Legendre-spectral method based on the Legendre integration Gauss points and Lagrange interpolation is proposed to convert the nonlinear integral equations to a nonlinear system of equations where the solution leads to the values of unknown functions at collocation points.

We study a spline wavelet alternative direction implicit (SW-ADI) algorithm for solving two-dimensional reaction diffusion equations. This algorithm is based on a collocation method for PDEs with a specially designed spline wavelet for the Sobolev space H 2(I ) on a closed interval I. By using the tensor product nature of adaptive wavelet meshes, we propose a SW-ADI method for two-dimensional p...

Properties of the hybrid of block-pulse functions and Lagrange polynomials based on the Legendre-Gauss-type points are investigated and utilized to define the composite interpolation operator as an extension of the well-known Legendre interpolation operator. The uniqueness and interpolating properties are discussed and the corresponding differentiation matrix is also introduced. The appl...

Department of Mathematics and Sciences Dhofar University, Salalah Oman [email protected] Abstract Legendre wavelets methods are commonly used for the numerical solution of integral equations. In this paper, we apply the Legendre wavelets method to approximate the solution of fractional integro-differential equations. Numerical examples are also presented to demonstrate the validity of the method....