A -Stable Linear Multistep Methods for Volterra Integro-Differential Equations.
-stable methods of high order for Volterra integral equations
Method for numerical solution of Volterra integral equations, based on the O.I.M. methods, is suggested. It is known that the class of O.I.M. methods includes -stable methods of arbitrary high order of asymptotic accuracy. In part 5, it is proved that these methods generate methods for numerical solution of Volterra equations which are also -stable and of an arbitrarily high order. There is one advantage of the methods. Namely, they need no matrix inversion in the course of their numerical realization....
A study of the fast solution of the occluded radiosity equation.
A two-dimensional inverse heat conduction problem for estimating heat source.
A Unified Approach for Constructing Fast Two-Step Newton-like Methods.
A unifying convergence analysis of Newton's method for twice Fréchet-differentiable operators
We provide a local as well as a semilocal convergence analysis for Newton's method using unifying hypotheses on twice Fréchet-differentiable operators in a Banach space setting. Our approach extends the applicability of Newton's method. Numerical examples are also provided.
A well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition
The construction of a well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition is proposed. A suitable parametrix is obtained by using a new unknown and an approximation of the transparency condition. We prove the well-posedness of the equation for any wavenumber. Finally, some numerical comparisons with well-tried method prove the efficiency of the new formulation.
About calculation of the Hankel transform using preliminary wavelet transform.
About the deficient spline collocation method for particular differential and integral equations with delay.
Adaptive Boundary Element Methods for Strongly Elliptic Integral Equations.
Algebraic properties of refinable sets.
Algebras of approximation sequences: Fredholm theory in fractal algebras
The present paper is a continuation of [5, 7] where a Fredholm theory for approximation sequences is proposed and some of its properties and consequences are studied. Here this theory is specified to the class of fractal approximation methods. The main result is a formula for the so-called α-number of an approximation sequence (Aₙ) which is the analogue of the kernel dimension of a Fredholm operator.
Algorithm 65. Determination of the solution of an Abel integral equation
Algorithm 67. Determination of the solution of Abel integral equations, II
Algorithm 68. Determination of the solution of Abel integral equations, III
Algorithm for reconstruction of the elastic constants of an anisotropic layer lying in an isotropic horizontally stratified medium.
An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data
We propose an adaptive finite element method for the solution of a linear Fredholm integral equation of the first kind. We derive a posteriori error estimates in the functional to be minimized and in the regularized solution to this functional, and formulate corresponding adaptive algorithms. To do this we specify nonlinear results obtained earlier for the case of a linear bounded operator. Numerical experiments justify the efficiency of our a posteriori estimates applied both to the computationally...
An Adaptive Numerical Method for Solving Linear Fredholm Integral Equations of the First Kind.
An Algorithm for the Hausdorff Moment Problem.
An Algorithm for the Numerical Evaluation of Certain Cauchy Principal Value Integrals.