Abstract. It was shown by P. J. Davis that the Newton-Cotes quadrature formula is convergent if the integrand is an analytic function that is regular in a sufficiently large region of the complex plane containing the interval of integration. In the present paper, a bound on the error of the Newton-Cotes quadrature formula for analytic functions is derived. Also the bounds on the Legendre polyno...

We state and prove an apparently hitherto unrecorded evaluation of certain Legendre symbols: if p is prime, p 6= 2, and ab = p − 1, then the Legendre symbol ( b p ) is given by ( b p ) = (−1).

we consider an approximation scheme using haar wavelets for solving a class of infinite horizon optimal control problems (ocp's) of nonlinear interconnected large-scale dynamic systems. a computational method based on haar wavelets in the time-domain is proposed for solving the optimal control problem. haar wavelets integral operational matrix and direct collocation method are utilized to ...

In this work, wavelets are used in the analysis of medical images, where efficiency mathematics field has been proven because basis proposed work is newly constructed mathematical equations, and through MATLAB program, many programs have designed to be ready for use image study. Physical samples were selected that compressed using wavelets, good results obtained prove method used.

In this paper, we introduce vector-valued multiresolution analysis and vector-valued wavelets for vector-valued signal spaces. We construct vector-valued wavelets by using paraunitary vector lter bank theory. In particular, we construct vector-valued Meyer wavelets that are band-limited. We classify and construct vector-valued wavelets with sampling property. As an application of vector-valued ...

A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operat...

This paper presents the use of Legendre pseudospectral method for the optimization of finite-thrust orbital transfer for spacecrafts. In order to get an accurate solution, the System’s dynamics equations were normalized through a dimensionless method. The Legendre pseudospectral method is based on interpolating functions on Legendre-Gauss-Lobatto (LGL) quadrature nodes. This is used to transfor...

In this article, a shifted Legendre tau method is introduced to get a direct solution technique for solving multi-order fractional differential equations (FDEs) with constant coefficients subject to multi-point boundary conditions. The fractional derivative is described in the Caputo sense. Also, this article reports a systematic quadrature tau method for numerically solving multi-point boundar...