โ Scribed by Andrew W. Gill; G.E. Sneddon
No coin nor oath required. For personal study only.
The rate of convergence of the pseudospectral approximation to singular linear differential eigenproblems is asymptotically geomettropic model of tropical cyclones for various velocity proric, but is often seriously weakened by the presence of singularities, files. Both methods became increasingly inaccurate at the called critical points or critical latitudes. One remedy is to implement upper limit of unstable wavenumbers where the critical an independent variable transformation which distorts the computapoints approach the computational domain. This problem tional domain into the complex plane and away from the critical does not arise at the lower limit of unstable wavenumbers point. These complex maps can then be chosen to minimize the effect of the critical points. However, the degree of improvement is because as the wave speed approaches zero, the critical limited for critical points near a boundary point, since each contour point does not approach the real axis (for example, see [1]).
produced by the complex maps must terminate there to enforce
The use of complex maps as a remedy to this problem the boundary conditions. In this paper, new complex maps are was initially suggested by Boyd and Christidis [4]. The developed for problems containing a single near-boundary critical point. These new composite complex maps are polynomials of de-complex map is an independent variable transformation gree 2 p , where p ี 1 is the level of composition. Formulae for the which distorts the computational domain into one in the optimal map parameters are deduced analytically and indicate that complex plane, so that the effect of the singularities on significant acceleration of the geometric rate of convergence is posthe rate of convergence of the numerical schemes is minisible. A test problem is solved to illustrate the technique. Although mized. Its use was investigated in some detail by Boyd [5] successful, it is shown that previously ignored algebraic factors in the formula for the error may become significant when utilizing and subsequently by Gill and Sneddon. While it has been composite complex maps.
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The completion of a preliminary human genome map and development of molecular methods have enabled researchers to assay a large number of polymorphic markers that are evenly spaced along the entire human genome. Among many applications, marker data are valuable for mapping complex traits through lin