For {φ_n(x)}, x ε [0,1] an orthonormalsystem of uniformly bounded functions, ||φ_n||_{∞}≤ M

in this article the nonlinear mixed volterra-fredholm integral equations are investigated by means of the modied three-dimensional block-pulse functions (m3d-bfs). this method converts the nonlinear mixed volterra-fredholm integral equations into a nonlinear system of algebraic equations. the illustrative   examples are provided to demonstrate the applicability and simplicity of our   scheme.

a numerical method for solving variational problems is presented in this paper. the method is based upon hybrid of hartley functions approximations. the properties of hybrid functions which are the combinations of block-pulse functions and hartley functions are first presented. the operational matrix of integration is then utilized to reduce the variational problems to the solution of algebraic...

In this paper, time series prediction is considered as a problem of missing values. A new method for the determination of the missing time series values is presented. The new method is based on two projection methods: a nonlinear one (Self-Organized Maps) and a linear one (Empirical Orthogonal Functions). The presented global methodology combines the advantages of both methods to get accurate c...

in this paper, we introduce hybrid of block-pulse functions and bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. then, we utilize them to solvedelay differential equations and time-delay system. the method is based upon ex...

This report presents a Bayesian version of empirical orthogonal functions (EOFs) and thereby overcomes a difficulty with the classical version of these functions when an environmental process is autocorrelated as most are. The approach partitions the spatial variation into long and short scale variation, the latter including measurement errors. The most general version of our results incorporat...

Using satellite-observed Normalized Difference Vegetation Index (NDVI) data and Rotated Empirical Orthogonal Function (REOF) method, we analyzed the spatio-temporal variation of vegetation during growing seasons from May to September in the Three-River Source Region, alpine meadow in the QinghaiTibetan Plateau from 1982 to 2006. We found that NDVI in the centre and east of the region, where the...

in this study, the problem of determining an optimal trajectory of a nonlinear injection into orbit problem with minimum time was investigated. the method was based on orthogonal polynomial approximation. this method consists of reducing the optimal control problem to a system of algebraic equations by expanding the state and control vector as chebyshev or legendre polynomials with undetermined...

in this paper, we introduce a family of fractional-order chebyshev functions based on the classical chebyshev polynomials. we calculate and derive the operational matrix of derivative of fractional order $gamma$ in the caputo sense using the fractional-order chebyshev functions. this matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...