High order compact schemes

M. H. Carpenter, D. Gottlieb, and S. Abarbanel, Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems Methodology and application to high-order compact schemes, / Comput. Phys., vol. Ill, no. 2, pp. 220-236, Apr. 1994. doi 10.1006/jcph. 1994.1057... 

S. S. Abarbanel and A. E. Chertock. Strict stability of high-order compact implicit finite-difference schemes the role of boundary conditions for hyperbolic PDEs, I. J. Comput. Phys., 160 42-66, 2000. 

J. S. Shang, High-order compact-difference schemes for time-dependent Maxwell equations, / Comput. Phys., vol. 153, no. 1, pp. 312—333, July 1999. 

As had been predicted prior to the determination of the X-ray structure, the proteinase assembles its catalytic machinery using a C2 symmetric homodimer (as opposed to a monomer in renin). The symmetrical nature of the enzyme suggested that C2 symmetric inhibitors might be effective. The X-ray structure also revealed the presence of an ordered water molecule bound to two of the carbonyl groups of the inhibitor. Displacement of such a water molecule with an inhibitor should, theoretically, lead to greatly enhanced activity. This theory was exploited with a class of cyclic inhibitors that mimicked the interactions of the water molecule with functionality within the inhibitor leading to highly potent and compact inhibitors, e.g., XM-323 (see Scheme 9) (15). 

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