An Unconditionally Stable Scheme for the Numerical Solution of Finite Difference Forms of Poisson's Equation

A procedure for an unconditionally stable non-iterative step-by-stepscheme for the solution of second order ordinary boundary valuedifference equations is extended to Poisson's equation withDirichlet boundary conditions. It is shown that owing to theparticular method of solution rounding error from a particulargrid point has practically no effect on other grid points, andit is absolutely stable for all finite difference forms of Poisson'sequation. The extension to other two dimensional partial differentialequations is discussed. It is also shown that the scheme isparticularly valuable in problems in which a high degree ofaccuracy is demanded and it is recommended for numerical weatherexperiments.     

Mathematical modeling of a continuous-flow packed-bed reactor with immobilized lipase for kinetic resolution of (R,S)-2-pentanol

In this study, the kinetic resolution of (R,S)-2-pentanol via transesterification to achieve S-2-pentanol, a key intermediate required in the synthesis of anti-Alzheimer drugs, was investigated in continuous-flow packed-bed reactors. The effects of residence time, substrate concentration, and operation time of the enzyme were investigated. Under steady state conditions, 50% conversion and enantiomeric excess of the substrate (ee _S >99% were achieved at a residence time of 0.04 min. Productivity of the continuous-flow process (1.341 mmol/min/g)was about 4 times higher than that of the corresponding batch process (0.363 mmol/min/g). In addition, the mathematical modeling of the packed-bed reactor was conductedusing an axial dispersion model. Ping Pong Bi Bi kinetics was used in this model. Design parameters were determined and the developed equations were solved using an algorithm for solving boundary value problems for ordinary differential equations by collocation (bvp4c) using MATLAB. The results, obtained from the model, fitted the experimental data very well.)