Difference scheme higher-accuracy

Alekseevskii, M. (1984) Difference schemes of higher-order accuracy for some singular-perturbed boundary-value problems. Differential Equations, 17, 1177-1183 (in Russian). 

Bagmut, G. (1969) Difference schemes of higher-order accuracy for an ordinary differential equations with singularity. Zh. Vychisl. Mat. i Mat. Fiz., 9, 221-226 (in Russian) English transl. in USSR Comput. Mathem. and Mathem. Physics. 

Semiempirical methods are the middle ground between highly accurate ab initio methods and completely empirical molecular mechanical (MM) methods [155]. For the treatment of very large biomolecules, hybrid approaches have been developed where the reactive center is described by a semiempirical method and the inert rest of the molecule by a classical force field [3,156,157], This technique can also be applied for the description of solvent effects. The solvent molecules are then described by the MM method. If an even higher accuracy is required for the reactive center of the system, a hybrid approach of three different methods can be applied, e.g., in the ONIOM model by Vreven and Morokuma [158], Here the center is described at DFT or post-HF level, the nearest-neighbor atoms at semiempirical level, and the outer surrounding at MM level. There also exist hybrid schemes between semiempirical and DFT methods only [159],... 

Villadsen J, Michelsen ML (1978) Solution of Differential Equations Models by Polynomial Approximation. Prentice-Hall, Englewood Cliffs Warming RF, Hyett BJ (1974) The modified equation approach to the stability and accuracy analysis of finite-difference methods. J Comp Phys 14 159-179 Waterson NP, Deconinck H (2007) Deign principles for bounded higher-order convection schemes-a unified approach. J Comput Phys 224 182-207 Wesseling P (1992) An Introduction to Multigrid Methods. John Wiley Sons, New York... 

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