摘要:

AbstractNumerical methods for solving the heat equation via potential theory have been hampered by the high cost of evaluating heat potentials. WhenMpoints are used in the discretization of the boundary andNtime steps are computed, an amount of work of the orderO(N2M2) has traditionally been required. In this paper, we present an algorithm which requires an amount of work of the orderO(NM), and we observe speedups of five orders of magnitude for large‐scale problems. Thus, the method makes it possible to solve the heat equation by potential theory in practical situation

ISSN:0010-3640    

DOI:10.1002/cpa.3160430802

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1990

数据来源: WILEY

摘要:

AbstractWe prove consistency, stability, and convergence of a point vortex approximation to the 3‐D incompressible Euler equations with smooth solutions. The 3‐D algorithm we consider here is similar to the corresponding 3‐D vortex blob algorithm introduced by Beale and Majda; see [3]. We first show that the discretization error is second‐order accurate. Then we show that the method is stable inlpnorm for the particle trajectories and inw−1.pnorm for discrete vorticity. Consequently, the method converges up to any time for which the Euler equations have a smooth solution. One immediate application of our convergence result is that the vortex filament method without smoothing also

ISSN:0010-3640    

DOI:10.1002/cpa.3160430803

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1990

数据来源: WILEY

摘要:

AbstractWe study the limiting behavior of the solution of\documentclass{article}\pagestyle{empty}\begin{document}$$ u_1 - \varepsilon ^2 u_{xx} + u^3 - u = 0,\,\,\,\,\,\,\,\,\,\,a < x < b, $$\end{document}with a Neumann boundary condition or an appropriate Dirichlet condition. The analysis is based on “energy methods”. We assume that the initial data has a “transition layer structure”, i.e.,uϵ≈ ±+M 1 except near finitely many transition points. We show that, in the limit as ϵ → 0, the solution maintains its transition layer structure, and the transition points move slower than

ISSN:0010-3640    

DOI:10.1002/cpa.3160430804

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1990

数据来源: WILEY

摘要:

AbstractWe show how it is possible to approximate the Mumford‐Shah (see [29]) image segmentation functionalby elliptic functionals defined on Sobolev spaces. The heuristic idea is to consider functionals

ISSN:0010-3640    

DOI:10.1002/cpa.3160430805

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1990

数据来源: WILEY

摘要:

AbstractWe use weakly nonlinear asymptotics to derive a canonical asymptotic equation for rotationally invariant hyperbolic waves. The equation can include weak dissipative, dispersive, or diffractive effects. We give applications to equations from magnetohydrodynamics, elasticity, and viscoelasticity.

ISSN:0010-3640    

DOI:10.1002/cpa.3160430806

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1990

数据来源: WILEY

摘要:

AbstractThe author gives Diophantine definitions for polynomial rings of characteristicp>0 over the polynomial rings with constants in finite fields, and for rational integers over polynomial rings of characteristic 0. The author also investigates Diophantine relationships between other pairs of polynomial rings of characteristicp>0.

ISSN:0010-3640    

DOI:10.1002/cpa.3160430807

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1990

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160430801

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1990

数据来源: WILEY