in this paper, a numerical efficient method is proposed for the solution of time fractionalmobile/immobile equation. the fractional derivative of equation is described in the caputosense. the proposed method is based on a finite difference scheme in time and legendrespectral method in space. in this approach the time fractional derivative of mentioned equationis approximated by a scheme of order o...

In this report, we present two mathematical results which can be useful in a variety of settings. First, we present an analysis of Legendre polynomials triple product integral. Such integrals arise whenever two functions are multiplied, with both the operands and the result represented in the Legendre polynomial basis. We derive a recurrence relation to calculate these integrals analytically. W...

Let be introduced the Sobolev-type inner product (f, g) = 1 2 Z 1 −1 f(x)g(x)dx + M [f ′(1)g′(1) + f ′(−1)g′(−1)], where M ≥ 0. In this paper we will prove that for 1 ≤ p ≤ 4 3 there are functions f ∈ L([−1, 1]) whose Fourier expansion in terms of the orthonormal polynomials with respect to the above Sobolev inner product are divergent almost everywhere on [−1, 1]. We also show that, for some v...

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 an effective local error control algorithm for RK5GL3, which uses local extrapolation with an eighth-order Runge-Kutta method in tandem with RK5GL3, and a ...

In this correspondence we determine the linear complexity of all Legendre sequences and the (monic) feedback polynomial of the shortest linear feedback shift register that generates such a Legendre sequence. The result of this correspondence shows that Legendre sequences are quite good from the linear complexity viewpoint.

We consider the problem of recovering polynomials that are sparse with respect to the basis of Legendre polynomials from a small number of random samples. In particular, we show that a Legendre s-sparse polynomial of maximal degree N can be recovered fromm s log(N) random samples that are chosen independently according to the Chebyshev probability measure dν(x) = π−1(1 − x2)−1/2dx. As an effici...

‎in this paper‎, ‎we construct a new iterative method for solving nonlinear volterra integral equation of second kind‎, ‎by approximating the legendre polynomial basis‎. ‎error analysis is worked using banach fixed point theorem‎. ‎we compute the approximate solution without using numerical method‎. ‎finally‎, ‎some examples are given to compare the results with some of the existing methods‎.

in this paper, an effective technique is proposed to determine thenumerical solution of nonlinear volterra-fredholm integralequations (vfies) which is based on interpolation by the hybrid ofradial basis functions (rbfs) including both inverse multiquadrics(imqs), hyperbolic secant (sechs) and strictly positive definitefunctions. zeros of the shifted legendre polynomial are used asthe collocatio...

A fast, simple, and numerically stable transform for converting between Legendre and Chebyshev coefficients of a degree N polynomial in O(N(logN)2/ log logN) operations is derived. The basis of the algorithm is to rewrite a well-known asymptotic formula for Legendre polynomials of large degree as a weighted linear combination of Chebyshev polynomials, which can then be evaluated by using the di...