An adaptive mesh refinement method for solving optimal control problems is developed. The method employs orthogonal collocation at Legendre-Gauss-Radau points, and adjusts both the mesh size and the degree of the approximating polynomials in the refinement process. A previously derived convergence rate is used to guide the refinement process. The method brackets discontinuities and improves sol...

The mathematical modeling of a Pressure Swing Adsorption (PSA) system is discussed in detail for the Skarstrom cycle of two-bed process. The system is used to get pure oxygen product from the air with the use of zeolite 13X as an adsorbent. There are complex partial differential equations (pdes) which may not solve by analytical methods. There is no provision for solving it in any other softwar...

A pertraction membrane plant is designed for the treatment of wastewater containing hexavalent chromium and its recovery for industrial reuse. Pertraction is a new technology that combines the efficiency of emulsion liquid membranes with the advantages of using hollow fibber membrane modules. It can selectively remove low concentrated metals from process streams and reach high concentrations of...

Two discrete-time orthogonal spline collocation schemes are formulated and analyzed for solving the linear time-dependent Schrr odinger equation in two space variables. These are Crank-Nicolson and alternating direction implicit (ADI) schemes employing C 1 piecewise polynomial spaces of arbitrary degree 3 in each space variable. The stability of the schemes is examined and optimal order a prior...

We examine the use of orthogonal spline collocation for the semi-discretization of the cubic Schrr odinger equation and the two-dimensional parabolic equation of Tappert. In each case, an optimal order L 2 estimate of the error in the semidiscrete approximation is derived. For the cubic Schrr odinger equation, we present the results of numerical experiments in which the integration in time is p...

This paper presents a collocation method with an iterative linear system solver to compute periodic solutions of a system of autonomous delay differential equations (DDEs). We show that the linearized collocation system is equivalent to a discretization of the linearized periodic boundary value problem (BVP). This linear BVP is solved using the Newton-Picard single shooting method ([Int. J. Bif...