equations (cf. [AKT1]), the exact WKB analysis provides us with a powerful tool for studying global behavior of solutions of linear ordinary di erential equations. To generalize such an analysis to nonlinear equations, T. Kawai (RIMS, Kyoto Univ.), T. Aoki (Kinki Univ.) and the author have developed the WKB theory for Painlev e equations with a large parameter in our series of articles ([KT1], ...

Flame sheet problems are on the natural route to the numerical solution of detailed chemistry, laminar di usion ames, which, in turn, are important in many engineering applications. In order to model the ame structure more accurately, we use the vorticity-velocity formulation of the uid ow equations instead of the more traditional stream function-vorticity approach. The numerical solution of th...

We study accuracy of alternating direction implicit (ADI) methods for parabolic equations. The original ADI method applied to parabolic equations is a perturbation of the Crank-Nicolson di erence equation and has second-order accuracy both in space and time. The perturbation error is on the same order as the discretization error, in terms of mathematical description. However, we often observe i...

We establish L convergence of a viscous splitting method for nonlinear possibly strongly degenerate convection-di usion problems. Since we allow the equations to be strongly degenerate, solutions can be discontinuous and they are not, in general, uniquely determined by their data. We thus consider entropy weak solutions realized by the vanishing viscosity method. This notion is broad enough to ...

This paper surveys recent results on the classi cation of di erential invari ants of transformation groups and their applications to invariant di erential equations and variational problems Consider a group of transformations acting on a jet space coordinatized by the inde pendent variables the dependent variables and their derivatives Scalar functions which are not a ected by the group transfo...

Multidimensional wave digital lters yield robust algorithms for the computer simulation of certain distributed parameter systems described by partial di erential equations. Here, a multidimensional wave digital lter algorithm for the spacetime discretization of the physical laws of acoustics is discussed. Its implementation by state equations is presented. An example for the propagation of a so...

In this Note we present new results which bring about hitherto unknown relations between certain Bernstein di¤usions wandering in bounded convex domains of Euclidean space on the one hand, and processes which typically occur in forward-backward systems of stochastic di¤erential equations on the other hand. A key point in establishing such relations is the fact that the Bernstein di¤usions we co...

The e ciency of numerically solving time-dependent partial di erential equations on parallel computers can be greatly improved by computing the solution on many time-levels simultaneously. The theoretical properties of one such method, namely the discrete-time multigrid waveform relaxation method, are investigated for systems of ordinary di erential equations obtained by spatial nite element di...

The torsion modified Maxwell-Proca equations when applied to describe a plasma is shown to lead to a correction to the Debye screening length. For hot new born neutron stars the torsion correction is shown to be significant. This effect may provide an indirect evidence for Torsion. Indian Institute of Astrophysics, Bangalore India, and Universita degli Studi di Ferrara, Dipartimento di Fisica, ...

An exact solution of a system of coupled di erential equations describing the dynamics of a special class of winner-take-all networks is given. From the solution two properties of the short-termmemory traces are derived: (1) information preservation and (2) a discrimination measure. These properties justify a biologically inspired fault tolerant extension of the network using di erentiating neu...