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The pentadiagonal compact finite difference scheme and asymmetric boundary schemes are optimized with high accuracy and maximum resolution in this paper. Through Fourier analysis, the optimization is reduced to the problem of finding the minimum of a multivariable nonlinear function with multiple constraints. The advanced sequential quadratic programming method is employed to find the minimum. In order to extend the resolution characteristic of the schemes, the wavenumber domain for optimization is nearly identical to the well-resolved domain, and the maximum well-resolved wavenumber is obtained by means of equal step length searching. The optimized schemes are strictly stable as confirmed by an eigenvalue analysis. The increased performances of the schemes are demonstrated through their application to one-and twodimensional examples and are compared with other schemes optimized before.

To develop biodegradable polymers with favorable physicochemical and biological properties, we have synthesized a series of poly(terephthalate-co-phosphate)s using a two-step polycondensation. The diol 1,4-bis(2-hydroxyethyl) terephthalate was first reacted with ethylphosphorodichloridate (EOP), and then chain-extended with terephthaloyl chloride (TC). Incorporation of phosphate into the poly(ethylene terephthalate) backbone rendered the co-polymers soluble in chloroform and biodegradable, lowered the T g , decreased the crystallinity and increased the hydrophilicity. With an EOP/TC molar feed ratio of 80 : 20, the polymer exhibited good film-forming property, yielding at 86.6 ± 1.6% elongation with an elastic modulus of 13.76 ± 2.66 MPa. This polymer showed a favorable toxicity profile in vitro and good tissue biocompatibility in the muscular tissue of mice. In vitro the polymer lost 21% of mass in 21 days, but only 20% for up to 4 months in vivo. It showed no deterioration of properties after sterilization by γ -irradiation at 2.5 Mrad on solid CO 2 . Release of FITC-BSA from the microspheres was diffusion-controlled and exceeded 80% completion in two days. Release of the hydrophobic cyclosporine-A from microspheres was however much more sustained and near zero-ordered, discharging 60% in 70 days. A limited structure-property relationship has been established for this co-polymer series. The co-polymers became more hydrolytically labile as the phosphate component (EOP) was increased and the side chains were switched from the ethoxy to the methoxy structure. Converting the methoxy group to a sodium salt further increased the degradation rate significantly. The chain rigidity as reflected in the T g values of the co-polymers decreased according to the following diol structure in the backbone: ethylene glycol > 2-methylpropylene diol > 2,2-dimethylpropylene diol. The wide range of physicochemical properties obtainable from this co-polymer series should help the design of degradable biomaterials for specific biomedical applications.