739 research outputs found
Inversion of the Laplace transform from the real axis using an adaptive iterative method
In this paper a new method for inverting the Laplace transform from the real
axis is formulated. This method is based on a quadrature formula. We assume
that the unknown function is continuous with (known) compact support. An
adaptive iterative method and an adaptive stopping rule, which yield the
convergence of the approximate solution to , are proposed in this paper.Comment: 38 pages, 12 figure
Creating materials with a desired refraction coefficient: numerical experiments
A recipe for creating materials with a desired refraction coefficient is
implemented numerically. The following assumptions are used: \bee
\zeta_m=h(x_m)/a^\kappa,\quad d=O(a^{(2-\kappa)/3}),\quad
M=O(1/a^{2-\kappa}),\quad \kappa\in(0,1), \eee where and are
the boundary impedance and center of the -th ball, respectively, , Im, is the number of small balls embedded in the cube
, is the radius of the small balls and is the distance between the
neighboring balls.
An error estimate is given for the approximate solution of the many-body
scattering problem in the case of small scatterers. This result is used for the
estimate of the minimal number of small particles to be embedded in a given
domain in order to get a material whose refraction coefficient approximates
the desired one with the relative error not exceeding a desired small quantity.Comment: 24 page
Dynamical Systems Method for solving ill-conditioned linear algebraic systems
A new method, the Dynamical Systems Method (DSM), justified recently, is
applied to solving ill-conditioned linear algebraic system (ICLAS). The DSM
gives a new approach to solving a wide class of ill-posed problems. In this
paper a new iterative scheme for solving ICLAS is proposed. This iterative
scheme is based on the DSM solution. An a posteriori stopping rules for the
proposed method is justified. This paper also gives an a posteriori stopping
rule for a modified iterative scheme developed in A.G.Ramm, JMAA,330
(2007),1338-1346, and proves convergence of the solution obtained by the
iterative scheme.Comment: 26 page
An iterative method for solving Fredholm integral equations of the first kind
The purpose of this paper is to give a convergence analysis of the iterative
scheme: \bee u_n^\dl=qu_{n-1}^\dl+(1-q)T_{a_n}^{-1}K^*f_\dl,\quad
u_0^\dl=0,\eee where with finite-dimensional approximations of
and for solving stably Fredholm integral equations of the first kind with
noisy data.Comment: 29 page
A collocation method for solving some integral equations in distributions
A collocation method is presented for numerical solution of a typical
integral equation Rh :=\int_D R(x, y)h(y)dy = f(x), x {\epsilon} D of the class
R, whose kernels are of positive rational functions of arbitrary selfadjoint
elliptic operators defined in the whole space R^r, and D \subset R^r is a
bounded domain. Several numerical examples are given to demonstrate the
efficiency and stability of the proposed method.Comment: 26 pages, 4 figure
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