共查询到20条相似文献,搜索用时 12 毫秒
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By considering tridiagonal matrices as three-term recurrence relations with Dirichlet boundary conditions, one can formulate their inverses in terms of Green's functions. This analysis is applied to three-point difference schemes for 1-D problems, and five-point difference schemes for 2-D problems. We derive either an explicit inverse of the Jacobian or a sharp estimate for both uniform and nonuniform grids. 相似文献
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Erik Jarl Pickett 《Journal of Number Theory》2009,129(7):1773-1785
Let K be a finite extension of Qp, let L/K be a finite abelian Galois extension of odd degree and let OL be the valuation ring of L. We define AL/K to be the unique fractional OL-ideal with square equal to the inverse different of L/K. For p an odd prime and L/Qp contained in certain cyclotomic extensions, Erez has described integral normal bases for AL/Qp that are self-dual with respect to the trace form. Assuming K/Qp to be unramified we generate odd abelian weakly ramified extensions of K using Lubin-Tate formal groups. We then use Dwork's exponential power series to explicitly construct self-dual integral normal bases for the square-root of the inverse different in these extensions. 相似文献
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This paper investigates the multiplicity of positive solutions for a class of nonlinear boundary-value problems of fourth-order differential equations with integral boundary conditions in ordered Banach spaces. The arguments are based upon a specially constructed cone and the fixed point index theory in cone for strict set contraction operator. The nonexistence of positive solution is also studied. Meanwhile, an example is worked out to demonstrate the main results. 相似文献
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A. L. Kalamkarov B. A. Kudryavtsev V. Z. Parton 《Journal of Applied Mathematics and Mechanics》1991,55(6):844-852
An elliptic equation for a layered regularly inhomogeneous (composite) material serves as an example for the introduction of new integral transforms that enable boundary-value problems to be solved in quadratures, without the need to solve boundary-layer problems. These integral transforms are used to solve simple boundary-value problems for a layered composite and to obtain a fundamental solution of an elliptic equation in an infinite two-dimensional laminar medium. 相似文献
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An algebraic collocation method for approximating solutions of systems of nonlinear ordinary differential equations is shown to be applicable in the case of linear multipoint boundary conditions containing definite integrals.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 11, pp. 1548–1555, November, 1992. 相似文献
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The Schwarz method can be used for the iterative solution of elliptic boundary value problems on a large domain Ω. One subdivides
Ω into smaller, more manageable, subdomains and solves the differential equation in these subdomains using appropriate boundary
conditions. Optimized Schwarz Methods use Robin conditions on the artificial interfaces for information exchange at each iteration,
and for which one can optimize the Robin parameters. While the convergence theory of classical Schwarz methods (with Dirichlet
conditions on the artificial interface) is well understood, the overlapping Optimized Schwarz Methods still lack a complete
theory. In this paper, an abstract Hilbert space version of the Optimized Schwarz Method (OSM) is presented, together with
an analysis of conditions for its geometric convergence. It is also shown that if the overlap is relatively uniform, these
convergence conditions are met for Optimized Schwarz Methods for two-dimensional elliptic problems, for any positive Robin
parameter. In the discrete setting, we obtain that the convergence factor ρ(h) varies like a polylogarithm of h. Numerical experiments show that the methods work well and that the convergence factor does not appear to depend on h. 相似文献
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V. L. Vereshchagin 《Mathematical Notes》2013,93(3-4):360-372
Two nonlinear integrable models with two space variables and one time variable, the Kadomtsev-Petviashvili equation and the two-dimensional Toda chain, are studied as well-posed boundary-value problems that can be solved by the inverse scattering method. It is shown that there exists a multitude of integrable boundary-value problems and, for these problems, various curves can be chosen as boundary contours; besides, the problems in question become problems with moving boundaries. A method for deriving explicit solutions of integrable boundary-value problems is described and its efficiency is illustrated by several examples. This allows us to interpret the integrability phenomenon of the boundary condition in the traditional sense, namely as a condition for the availability of wide classes of solutions that can be written in terms of well-known functions. 相似文献
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This paper examines the estimation of an indirect signal embedded in white noise for the spherical case. It is found that the sharp minimax bound is determined by the degree to which the indirect signal is embedded in the linear operator. Thus, when the linear operator has polynomial decay, recovery of the signal is polynomial, whereas if the linear operator has exponential decay, recovery of the signal is logarithmic. The constants are determined for these classes as well. Adaptive sharp estimation is also carried out. In the polynomial case a blockwise shrinkage estimator is needed while in the exponential case, a straight projection estimator will suffice. The framework of this paper include applications to medical imaging, in particular, to cone beam image reconstruction and to diffusion magnetic resonance imaging. Discussion of these applications are included. 相似文献
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S. Staněk 《Ukrainian Mathematical Journal》2008,60(2):277-298
We present existence principles for the nonlocal boundary-value problem (φ(u(p−1)))′=g(t,u,...,u(p−1), αk(u)=0, 1≤k≤p−1, where p ≥ 2, π: ℝ → ℝ is an increasing and odd homeomorphism, g is a Carathéodory function that is either regular or has singularities in its space variables, and α
k: C
p−1[0, T] → ℝ is a continuous functional. An application of the existence principles to singular Sturm-Liouville problems (−1)n(φ(u(2n−)))′=f(t,u,...,u(2n−1)), u(2k)(0)=0, αku(2k)(T)+bku(2k=1)(T)=0, 0≤k≤n−1, is given.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 2, pp. 240–259, February, 2008. 相似文献
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Virginia Alarcón Sergio Amat Sonia Busquier David J. López 《Journal of Computational and Applied Mathematics》2008
In this paper, a modified Steffensen's type iterative scheme for the numerical solution of a system of nonlinear equations is studied. Two convergence theorems are presented. The numerical solution of boundary-value problems by the multiple shooting method using the proposed iterative scheme is analyzed. 相似文献