The method of operational matrices is based on the Bernoulli and Shifted Legendre polynomials which used to solve Falkner-Skan equation. nonlinear differential equation converting a system equations solved using Mathematica®12, approximate solutions are obtained. efficiency these methods was studied by calculating maximum error remainder ( ), it found that their increases as increases. Moreover...

In this paper, we apply spectral method based on the Bernstein polynomials for solving a class of optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative. In the first step, we introduce the dual basis and operational matrix of product based on the Bernstein basis. Then, we get the Bernstein operational matrix for the Jumarie’s modified Riemann-Liouville fractio...

a numerical method for solving nonlinear fredholm-volterra integral equations of general type is presented. this method is based on replacement of unknown function by truncated series of well known chebyshev expansion of functions. the quadrature formulas which we use to calculate integral terms have been imated by fast fourier transform (fft). this is a grate advantage of this method which has...

We consider the Euler type integral associated to the configuration space of points on an elliptic curve, which is an analogue of the hypergeometric function associated to the configuration space of points on a projective line. We calculate the twisted homology group, with coefficients in the local system associated to a power function gα of an elliptic function g, and the intersection form. Ap...

Poisson statistics are traditionally used to estimate the mean and standard deviation of the mean in time-range realizations of received photon counts from stationary processes in incoherent-detection lidar systems. However, this approach must be modified if the process under study is measurably nonstationary to account for any additional (and potentially unanticipated) variability. We demonstr...