Similarity solutions for the flow of granular materials are constructed. Unlike previous work, the present approach can be applied to non-axisymmetric containers. The steady state equations are reduced to a nonlinear Helmholtz on a subdomain of the sphere. Existence and local uniqueness of the solutions are established. A spectral numerical method using Fourier/ChebyshevGauss-Radau collocation ...

This paper analyzes the stability and convergence of the Fourier pseudospectral method coupled with a variety of specially designed time-stepping methods of up to fourth order, for the numerical solution of a three dimensional viscous Burgers’ equation. There are three main features to this work. The first is a lemma which provides for an L2 and H 1 bound on a nonlinear term of polynomial type,...

The previously developed Gauss pseudospectral method is extended to the case of nonlinear infinite-horizon optimal control problems. First, the semi-infinite domain t ∈ [0,+∞) is transformed to the domain τ = [−1,+1). The first-order optimality conditions of NLP obtained from the pseudospectral discretization are then presented. These optimality conditions are related to the KKT multipliers of ...