The stabilized march technique is extended to nonlinear two-point boundary value problems via a new Generalized Brent Method for systems of nonlinear algebraic equations. The resulting algorithms can be used to solve systems of nonlinear rst-order ordinary di erential equations under partially separated nonlinear boundary conditions economically. Numerical results which compare the nonlinear st...

The principle of differential marginality for cooperative games states that the differential of two players’ payoffs does not change when the differential of these players’ productivities does not change. Together with two standard properties, efficiency and the null player property, differential marginality characterizes the Shapley value. For games that contain more than two players, we show ...

Once ReΨ and ImΨ are found from these two coupled di erential equations, the time-dependent probability density |Ψ| for a particle represented by the wave function Ψ can be calculated from |Ψ| = Ψ∗Ψ = (ReΨ) + (ImΨ), where the * denotes the complex conjugate. Our task, then, is to solve Equations (2) and (3) numerically, and this computational approach requires that the partial derivatives be ap...

To solve boundary value problems of stationary heat distribution in composite materials, one has to solve partial di¤erential equations with rapidly oscillating coe¢cients. These equations are in general impossible to solve numerically by standard methods. Instead, one wants to ...nd constant, effective conductivities and solve the corresponding boundary value problem to get an approximate solu...

This paper considers two related problems of state estimation and model validation for a class of uncertain linear systems. The main contribution of the paper is that it considers a general information structure which allows for discrete and continuous measurements as well as missing data. The results are given in terms of a recursive state estimator involving a jump Riccati di€erential equatio...

Coronal mass ejections (CMEs) can have a profound impact on the interplanetary medium and the near-earth environment. We discuss the feasibility of detecting coronal mass ejections at radio wavelengths with a groundbased instrument. In particular, we explore the possibility that a radio telescope employing Fourier synthesis imaging techniques can detect thermal bremsstrahlung emission from CMEs...

A parallel algorithm, which is derived directly from the Schwarz alternating algorithm with an overlapping domain decomposition, for solving boundary value problems of elliptic partial di€erential equations is analyzed. A new general analysis framework di€erent from Lions' ones is established to describe the recursive relations of error functions between approximate solutions and the exact solu...

Domain decomposition methods for the solution of semi-linear selfadjoint and non-selfadjoint singularly perturbed di erential equations are considered. An iterative domain decomposition algorithm suitable for parallelization is described and convergence of the algorithm is established. The implementation on a shared memory multiprocessor is described and numerical examples are presented to demo...

This special session emphasizes the dual roles of both theory and applications of dynamical systems and di↵erential equations to mathematical models in biology and medicine. Recent advances within mathematical ecology (including competition between species, predator-prey and cooperative systems, and evolutionary theory) will be presented alongside those for mathematical models in various fields...

The paper is devoted to the study of the relationship between integral manifolds of ordinary di erential equations and duck trajectories. We derive su cient conditions for the existence of continuous slow integral surfaces that are devided into stable and unstable parts and propose a method of construction of surfaces consisting of duck trajectories.