We propose a numerical method for solving nonlinear initial-value problems of Lane-Emden type. The method is based upon nonclassical Gauss-Radau collocation points, and weighted interpolation. Nonclassical orthogonal polynomials, nonclassical Radau points and weighted interpolation are introduced on arbitrary intervals. Then they are utilized to reduce the computation of nonlinear initial-value...

This article studies the formation mission design problem for commercial aircraft in presence of uncertainties. Specifically, it considers uncertainties departure times and fuel burn savings trailing aircraft. Given several flights, consists arranging them or solo flights finding trajectories that minimize expected value DOC flights. The is formulated as an optimal control a stochastic switched...

A computational approach with the aid of Linear Multistep Method (LMM) for numerical solution differential equations initial value problems or boundary conditions has appeared several times in literature due to its good accuracy and stability properties. The major objective this article is extend a multistep Partial Differential Equation (PDE) originating from fluid mechanics two-dimensional sp...

This study aims to solve the most general form of linear mixed Volterra-Fredholm integro-differential equations multi-fractional order in Caputo sense (MV-FIFDEs), which is solved by using orthogonal generalized Bernstein’s polynomial expansion with collocation and moment discrete weighted residual method under suitable conditions; then, Clenshaw-Curtis formula applied approximate integral term...