摘要:

AbstractWe consider the linear algebra of a pair of skewsymmetrical forms in the space of periodic functions defined by differential operators. By linear transform in the space of functions we reduce this pair to the simplest possible form. In this process, we prove the theorem of reduction in rather general context. © 1994 John Wiley&Sons, Inc

ISSN:0010-3640    

DOI:10.1002/cpa.3160470802

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

年代:1994

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160470803

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

年代:1994

数据来源: WILEY

摘要:

AbstractWe study the large time behavior in L1of the compressible, isentropic, viscous 1‐D flow. Under the assumption that the initial data are smooth and small, we show that the solutions are approximated by the solutions of a parabolic system, and in turn by diffusion waves, which are solutions of Burgers equations. Decay rates in L1are obtained. Our method is based on the study of pointwise properties in the physical space of the fundamental solution to the linearized system. © 1994 John Wiley&Sons, I

ISSN:0010-3640    

DOI:10.1002/cpa.3160470804

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

年代:1994

数据来源: WILEY

摘要:

AbstractWe consider approximation by partial time steps of a smooth solution of the Navier‐Stokes equations in a smooth domain in two or three space dimensions with no‐slip boundary condition. For smallk>0, we alternate the solution for timekof the inviscid Euler equations, with tangential boundary condition, and the solution of the linear Stokes equations for timek, with the no‐slip condition imposed. We show that this approximation remains bounded in H2,pand is accurate to orderkin Lpfor p>∞. The principal difficulty is that the initial state for each Stokes step has tangential velocity at the boundary generated during the Euler step, and thus does not satisfy the boundary condition for the Stokes step. The validity of such a fractional step method or splitting is an underlying principle for some computational methods. © 1994 John Wiley&S

ISSN:0010-3640    

DOI:10.1002/cpa.3160470805

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

年代:1994

数据来源: WILEY

摘要:

AbstractIn a recent paper (L. Greengard and V. Rokhlin,On the Numerical Solution of Two‐Point Boundary Value Problems.in Communications on Pure and Applied Mathematics, Volume XLIV, 1991, pages 419‐452). L. Greengard and V. Rokhlin introduce a numerical technique for the rapid solution of integral equations resulting from linear two‐point boundary value problems for second‐order ordinary differential equations. In this paper, we extend the method to systems of ordinary differential equations. After reducing the system of differential equations to a system of second kind integral equations, we discretize the latter via a high‐order Nyström scheme. A somewhat involved analytical apparatus is then constructed which allows for the solution of the discrete system usingO(N.p2.n3)operations withNthe number of nodes on the interval,pthe desired order of convergence, andnthe number of equations in the system. Thus, the advantages of the integral equation formulation (small condition number, insensitivity to boundary layers, insensitivity to endpoint singularities, etc.) are retained, while achieving a computational efficiency previously available only to finite difference or finite element methods.We in addition present a Newton method for solving boundary value problems for nonlinear first‐order systems in which each Newton iterate is the solution of a second kind integral equation; the analytical and numerical advantages of integral equations are thus obtained for nonlinear boundary value problems. © 1994 John Wi

ISSN:0010-3640    

DOI:10.1002/cpa.3160470806

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

年代:1994

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160470801

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

年代:1994

数据来源: WILEY