A -Stable Linear Multistep Methods for Volterra Integro-Differential Equations.
J. Matthys (1976/1977)
Numerische Mathematik
Ľubor Malina (1975)
Aplikace matematiky
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....
Atkinson, Kendall, Chien, David (2006)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Shidfar, A., Zakeri, A., Neisi, A. (2005)
International Journal of Mathematics and Mathematical Sciences
Ioannis K. Argyros (1995)
Monatshefte für Mathematik
I. K. Argyros, D. González (2015)
Applicationes Mathematicae
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.
Sébastien Pernet (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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.
Postnikov, E.B. (2003)
Journal of Applied Mathematics
Calió, F., Marchetti, E., Pavani, R. (2003)
Rendiconti del Seminario Matematico
W.L. Wendland, De-hao Yu (1988)
Numerische Mathematik
Wu, Bin (2004)
Lobachevskii Journal of Mathematics
Steffen Roch (2002)
Studia Mathematica
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.
R. Smarzewski, H. Malinowski (1979)
Applicationes Mathematicae
H. Malinowski, R. Smarzewski (1980)
Applicationes Mathematicae
H. Malinowski, R. Smarzewski (1980)
Applicationes Mathematicae
Karchevsky, A.L. (2007)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
Nikolay Koshev, Larisa Beilina (2013)
Open Mathematics
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...
R.J. Hanson, J.L. Phillips (1975)
Numerische Mathematik
G. Greaves (1982)
Numerische Mathematik
D.F. Paget, D. Elliott (1972)
Numerische Mathematik