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91.
Summary. A third-order accurate Godunov-type scheme for the approximate solution of hyperbolic systems of conservation laws is presented.
Its two main ingredients include: 1. A non-oscillatory piecewise-quadratic reconstruction of pointvalues from their given
cell averages; and 2. A central differencing based on staggered evolution of the reconstructed cell averages. This results in a third-order central scheme, an extension along the lines
of the second-order central scheme of Nessyahu and Tadmor \cite{NT}. The scalar scheme is non-oscillatory (and hence – convergent),
in the sense that it does not increase the number of initial extrema (– as does the exact entropy solution operator). Extension to systems is carried out by componentwise application of the scalar framework. In particular, we have the advantage that, unlike upwind schemes, no (approximate) Riemann
solvers, field-by-field characteristic decompositions, etc., are required. Numerical experiments confirm the high-resolution
content of the proposed scheme. Thus, a considerable amount of simplicity and robustness is gained while retaining the expected
third-order resolution.
Received April 10, 1996 / Revised version received January 20, 1997 相似文献
92.
When trains of impulse controls are present on the right-hand side of a system of ordinary differential equations, the solution
is no longer smooth and contains jumps which can accumulate at several points in the time interval. In technological and physical
systems the sum of the absolute value of all the impulses is finite and hence the total variation of the solution is finite.
So the solution at best belongs to the space BV of vector functions with bounded variation. Unless variable node methods are
used, the loss of smoothness of the solution would a priori make higher-order methods over a fixed mesh inactractive. Indeed
in general the order of -convergence is and the nodal rate is . However in the linear case -convergence rate remains but the nodal rate can go up to by using one-step or multistep scheme with a nodal rate up to when the solution belongs to . Proofs are given of error estimates and several numerical experiments confirm the optimality of the estimates.
Received March 15, 1996 / Revised version received January 3, 1997 相似文献
93.
Geetha Ramaswami 《BIT Numerical Mathematics》1997,37(2):465-471
In this paper, we derive a one-parameter family of symplectic Runge-Kutta-Nyström methods of order 2s-1 and a two-parameter family of symplectic Runge-Kutta methods of order 2s-2. 相似文献
94.
In this paper we approximate the solution of a linear initial-value problem, making use of a Schauder basis for certain Banach space associated with such a differential problem. In addition, we apply that results in order to calculate numerically the response from a structure modelled by a three degree-of-freedom mass–damper–spring system. 相似文献
95.
LIKAITAI HEYINNIAN XIANGYIMIN 《高校应用数学学报(英文版)》1994,9(1):11-30
This paper deals with the inertial manifold and the approximate inertial manifold concepts of the Navier-Stokes equations with nonhomogeneous boundary conditions and inertial algorithm. Furtheremore, we provide the error estimates of the approximate solutions of the Navier-Stokes Equations. 相似文献
96.
B. Abramovitz 《Acta Appl Math》1994,36(3):211-226
In this work, we consider the regularization method for linear ill-posed problems. For operators and approximating subspaces satisfying certain conditions and for a specific form of the regularization parameter, upper and lower bounds are given for the condition number of the corresponding discrete problem. 相似文献
97.
Numerous versions of the Lanczos τ-methods have been extensively used to produce polynomial approximations for functions verifying
a linear differential equation with polynomial coefficients. In the case of an initial-value problem, an adapted τ-method
based on Chebyshev series and the use of symbolic computation lead to a rational approximation of the solution on a region
of the complex plane. Numerical examples show that the simplicity of the method does not prevent a high accuracy of results.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
98.
We study a degenerate nonlinear variational inequality which can be reduced to a multivalued inclusion by an appropriate change
of the unknown function. We establish existence, uniqueness and regularity results. An application arising in the theory of
water diffusion in porous media is discussed as an example.
相似文献
99.
Herve Loïc 《Integral Equations and Operator Theory》1998,32(2):199-215
LetX be a locally compact space, andT, a quasi-compact positive operator onC
0(X), with positive spectral radius,r. Then the peripheral spectrum ofT is a finite set of poles containingr, and the residue of the resolvent ofT at each peripheral pole is of finite rank. Using the concept of closed absorbing set, we develop an iterative process that gives the order,p, ofr, some special bases of the algebraic eigenspaces ker(T-r)
p
and ker(T
*-r)
p
, and finally the dimension of the algebraic eigenspace associated to each peripheral pole. 相似文献
100.
Apart from specific methods amenable to specific problems, symplectic Runge-Kutta methods are necessarily implicit. The aim
of this paper is to construct explicit Runge-Kutta methods which mimic symplectic ones as far as the linear growth of the
global error is concerned. Such method of orderp have to bepseudo-symplectic of pseudosymplecticness order2p, i.e. to preserve the symplectic form to within ⊗(h
2p
)-terms. Pseudo-symplecticness conditions are then derived and the effective construction of methods discussed. Finally, the
performances of the new methods are illustrated on several test problems. 相似文献