A variable-step double-integration multi-step integrator is derived using divided differences. The derivation is based upon the derivation of Shampine-Gordon, a single-integration method. Variable-step integrators are useful for propagating elliptical orbits, because larger steps can be taken near apogee. As a double-integration method, the integrator performs only one function evaluation per s...

The paper presents two techniques to convert raster images in a Scalable Vector Graphics format. The first method is a technique that generates a Data Dependent Triangulation just by swapping the edges generated by a regular triangulation; the second technique is a Wavelet Based Triangulation and generates a multi-level triangulation based on the data collected from the wavelet multi-level tran...

Further to a recent controversy on whether or not the differential transformation method (DTM) for solving a differential equation is purely and solely the traditional Taylor series method, it is emphasized that the DTM is currently used as a technique for calculating the power series of the solution (in terms of the initial value parameters) including, sometimes, a piecewise analytic continuat...

A binomial lattice approach is proposed for valuing options whose payoff depends on multiple state variables following correlated geometric Brownian processes. The proposed approach relies on two simple ideas: a log-transformation of the underlying processes, which is step by step consistent with the continuous-time diffusions, and a change of basis of the asset span, to transform asset prices ...

SUMMARY Cumpsty and Head's entrainment method for turbulent boundary layers is extended to compressible flow using Green's compressibility assumptions. The laminar layer is predicted using Thwaites' method in the chordwise plane and the Nath method spanwise. The Rott compressibility transformation is used. The transition and wake assumptions are consistent with the two-dimensional profile drag ...