in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...

‎A numerical technique based on the collocation method using Legendre multiwavelets are‎ ‎presented for the solution of forced Duffing equation‎. ‎The operational matrix of integration for ‎Legendre multiwavelets is presented and is utilized to reduce the solution of Duffing equation‎ ‎to the solution of linear algebraic equations‎. ‎Illustrative examples are included to demonstrate‎ ‎the valid...

A directional spherical wavelet analysis is performed to examine the Gaussianity of the Wilkinson Microwave Anisotropy Probe (WMAP) 1-year data. Such an analysis is facilitated by the introduction of a fast directional continuous spherical wavelet transform. The directional nature of the analysis allows one to probe orientated structure in the data. Significant deviations from Gaussianity are d...

in this paper we present a method to perform flood frequency analysis (ffa) when the assumption of stationary is not important (or not valid). a wavelet transform model is developed to ffa. a full series is applied to ffa using two different wavelet functions, and then a combined method is investigated. in the combined method, all discharge data which were less than the lowest value of annual m...

In this paper, a novel technique for power amplifier (PA) linearization is presented. The Legendre wavelet neural networks (LWNN) is first utilized to model PA and inverse structure of the PA by applying practical transmission signals and the gradient descent algorithm is applied to estimate the coefficients of the LWNN. Secondly, this technique is implemented to identify and optimize the coeff...

Breast cancer has become the second leading cause of death among women worldwide. In India, a woman is diagnosed with breast every four minutes. There been no known basis behind it, and detection extremely challenging medical scientists researchers due to unknown reasons. ratio being identified in urban areas 22:1. Symptoms for this disease are micro calcification, lumps, masses mammogram image...

Mammography is the only effective and viable technique to detect breast cancer especially in the case of minimal tumors. About 30% to 50% of breast cancers demonstrate deposits of calcium called micro calcifications. Our method proposes an approach for detecting microcalcification in mammograms based on combined feature set with Support Vector Machine (SVM) classifier. The diagonal matrix ̳S‘ o...

In the present paper we study the Lie sphere geometry of Legendre surfaces by the method of moving frame and we prove an existence theorem for real-analytic Lie-minimal Legendre surfaces.

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,...