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911.
A control-theoretic approach is used to design a new automatic stepsize control algorithm for the numerical integration of ODE's. The new control algorithm is more robust at little extra expense. Its improved performance is particularly evident when the stepsize is limited by numerical stability. Comparative numerical tests are presented. 相似文献
912.
Let BG be the classifying space for stable spherical fibrations, and let V be a finite dimensional vector subspace of the cohomology algebra H1(BG; 2). We prove that V may be realized by a Poincaré duality space P, which means that if v:P→BG is the Spivak fibration, then v1 maps V isomorphically onto its image in H1(P;2). By construction, P is the product of a certain Grassman manifold and a spherical fiber space over a closed smooth manifold. 相似文献
913.
Seymour V. Parter 《Numerische Mathematik》1988,52(6):701-723
Summary TheMGR[v] algorithms of Ries, Trottenberg and Winter, the Algorithms 2.1 and 6.1 of Braess and the Algorithm 4.1 of Verfürth are all multigrid algorithms for the solution of the discrete Poisson equation (with Dirichlet boundary conditions) based on red-black Gauss-Seidel smoothing. Both Braess and Verfürth give explicit numerical upper bounds on the rate of convergence of their methods in convex polygonal domains. In this work we reconsider these problems and obtain improved estimates for theh–2h Algorithm 4.1 as well asW-cycle estimates for both schemes in non-convex polygonal domains. The proofs do not depend on the strengthened Cauchy inequality.Sponsored by the Air Force Office of Scientific Research under Contract No. AFOSR-86-0163 相似文献
914.
Herbert Arndt 《Numerische Mathematik》1980,36(1):99-107
Summary In this paper we consider rational interpolation for an Hermite Problem, i.e. prescribed values of functionf and its derivatives. The algorithm presented here computes a solutionp/q of the linearized equationsp–fq=0 in form of a generalized continued fraction. Numeratorp and denominatorq of the solution attain minimal degree compatible with the linearized problem. The main advantage of this algorithm lies in the fact that accidental zeros of denominator calculated during the algorithm cannot lead to an unexpected stop of the algorithm. Unattainable points are characterized.
Herrn Prof. Dr. Dr. h.c.mult. L. Collatz zum 70. Geburtstag gewidmet 相似文献
915.
916.
Felice Iavernaro Francesca Mazzia Donato Trigiante 《Mediterranean Journal of Mathematics》2005,2(1):53-69
We discuss the use of linear multistep methods for the solution of conservative (in particular Hamiltonian) problems. Despite the lack of good results concerning their behaviour, linear multistep methods have been satisfactorily used by researchers in applicative fields. We try to elucidate the requirements that a linear multistep method should fulfill in order to be suitable for the integration of such problems, relating our analysis to their use as boundary value methods. We collect a number of results obtained for the linear autonomous case and also consider some numerical tests on the Kepler problem.Work supported by GNCS and MIUR. 相似文献
917.
Stig Skelboe 《BIT Numerical Mathematics》1992,32(4):689-701
This paper presents a class of parallel numerical integration methods for stiff systems of ordinary differential equations which can be partitioned into loosely coupled sub-systems. The formulas are called decoupled backward differentiation formulas, and they are derived from the classical formulas by restricting the implicit part to the diagnonal sub-system. With one or several sub-systems allocated to each processor, information only has to be exchanged after completion of a step but not during the solution of the nonlinear algebraic equations.The main emphasis is on the formula of order 1, the decoupled implicit Euler formula. It is proved that this formula even for a wide range of multirate formulations has an asymptotic global error expansion permitting extrapolation. Besides, sufficient conditions for absolute stability are presented. 相似文献
918.
919.
920.
Ke-Qin Liu 《Letters in Mathematical Physics》1992,24(4):257-265
The q-analogues of some concepts in the theory of nonassociative algebras are introduced and two characterizations are given for the quantum Witt algebra. 相似文献