The purpose of the Air Transportation System (ATS) is to provide safe and efficient transportation of passengers and cargo. The on-time performance of the ATS is measured by flight-based metrics such as flight delays and flight cancellations. Researchers have shown that flight-based metrics do not accurately reflect the passenger trip experience, and especially underestimate the impacts of canc...

The ultimate goal of this study is to develop a numerically effective approximation technique acquire numerical solutions the integer and fractional-order Bratu singular Lane–Emden-type problems especially with exponential nonlinearity. Both initial boundary conditions were considered fractional derivative being in Liouville–Caputo sense. In direct approach, generalized Bessel matrix method bas...

<p style='text-indent:20px;'>Ordinary differential equations are converted into a constrained optimization problems to find their approximate solutions. In this work, an algorithm is proposed by applying particle swarm (PSO) solution of ODEs based on expansion approximation. Since many cases linear and nonlinear have singularity point, Padé approximant which fractional employed for more a...

Bratu's problem, which is the nonlinear eigenvalue equation Au + 2 exp(u)= 0 with u = 0 on the walls of the unit square and 2 as the eigenvalue, is used to develop several themes on applications of Chebyshev pseudospectral methods. The first is the importance of symmett:v: because of invariance under the C 4 rotation group and parity in both x and y, one can slash the size of the basis set by a...