Abstract We discuss optimal design problems for a popular method of series estimation in regression problems. Commonly used design criteria are based on the generalized variance of the estimates of the coefficients in a truncated series expansion and do not take possible bias into account. We present a general perspective of constructing robust and efficient designs for series estimators which ...

In this paper, a collocation method based on the Bernstein polynomials is presented for the fractional Riccati type differential equations. By writing t? ta (0 < a < 1) in the truncated Bernstein series, the truncated fractional Bernstein series is obtained and then it is transformed into the matrix form. By using Caputo fractional derivative, the matrix forms of the fractional derivatives are ...

Cone polynomials, also known as volume polynomials and/or spline polynomials, are the polynomials that appear in the local structure of the truncated powers, hence in the local structure of any derived construction such as box splines, simplex splines, character formulæ and moment maps. We provide a fresh look at bivariate cone polynomials. Two main principles underlie our approach here. The fi...

In the present study, the onset of double diffusive reaction-convection in a uid layer with viscous fluid, heated and salted from below subject to chemical equilibrium on the boundaries, has been investigated. Linear and nonlinear stability analysis have been performed. For linear analysis normal mode technique is used and for nonlinear analysis minimal representation of truncated Fourier serie...

A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equ...

The boundary value problem (BVP) for the varying coefficient linear Caputo-type fractional differential equation subject to mixed conditions on interval 0≤x≤1 was considered. First, BVP converted into an equivalent differential–integral merging conditions. Then, shifted Chebyshev polynomials and collocation method were used solve equation. Varying coefficients also decomposed truncated series s...