the low earth orbiting (leo) satellites are widely used for geosciences applications. for most applications, precise orbital information of the satellites is required. a combination of the in suite observations and dynamic orbit yields the optimum solution. in order to obtain the combined optimal solution, one needs to analytically or numerically propagate the state vector epoch by an epoch bas...

Boundary integral equations and Nyström discretization provide a powerful tool for the solution of Laplace and Helmholtz boundary value problems. However, often a weaklysingular kernel arises, in which case specialized quadratures that modify the matrix entries near the diagonal are needed to reach a high accuracy. We describe the construction of four different quadratures which handle logarith...

A collocation procedure is developed for the linear and nonlinear Fredholm and Volterra integral equations, using the globally defined B-spline and auxiliary basis functions. The solution is collocated by cubic B-spline and then the integral equation is approximated by the 5-points Gauss–Turán quadrature formula with respect to the Legendre weight function. Combination of these two approaches i...

We investigate a Gaussian quadrature rule and the corresponding orthogonal polynomials for the oscillatory weight function ei!x on the interval [ 1, 1]. We show that such a rule attains high asymptotic order, in the sense that the quadrature error quickly decreases as a function of the frequency !. However, accuracy is maintained for all values of ! and in particular the rule elegantly reduces ...

We complete and extend the asymptotic analysis of the spectrum of Jacobi Tau approximations that were first considered by Dubiner. The asymptotic formulas for Jacobi polynomials N P ( , ) , , 1 > − α β α β are derived and confirmed by numerical approximations. More accurate results for the slowest decaying mode are obtained. We explain where the large negative eigenvalues come from. Furthermore...

The Falkner-Skan equation arises in the study of laminar boundary layers exhibiting similarity. The MHD systems are used effectively in many applications including power generators, pumps, accelerators, electrostatic filters, droplet filters, the design of heat exchangers, the cooling of reactors, etc. For the MHD Falkner-Skan equation, we have developed a new numerical technique transforming t...

A semi-parametric mixed eeects regression model is proposed for the analysis of clustered or longitudinal data with continuous, ordinal or binary outcome. The commonly used Gaussian assumption on the random eeects distribution is relaxed as the partial predictive recursion method (Newton and Zhang, 1996) is used to estimate the random eeects density function. The parameter estimates are obtaine...