APPROXIMATE SOLUTION OF O.D.E.S IN BANACH SPACE - RATIONAL APPROXIMATION OF SEMIGROUPS

The aim of the paper is to prove a theorem about the existence of an approximate solution to an abstract nonlinear nonlocal Cauchy problem in a Banach space. The right-hand side of the nonlocal condition belongs to a locally closed subset of a Banach space. The paper is a continuation of papers [1], [2] and generalizes some results from [3].

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Approximate solution of a parabolic equation with the use of a rational approximation to the operator exponential

Differential Equations ◽

10.1134/s0012266117030107 ◽

2017 ◽

Vol 53 (3) ◽

pp. 398-408 ◽

Cited By ~ 4

Author(s):

M. N. Oreshina

Keyword(s):

Approximate Solution ◽

Parabolic Equation ◽

Rational Approximation ◽

Operator Exponential

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A Unified Formulation of Analytical and Numerical Methods for Solving Linear Fredholm Integral Equations

Algorithms ◽

10.3390/a14100293 ◽

2021 ◽

Vol 14 (10) ◽

pp. 293

Author(s):

Efthimios Providas

Keyword(s):

Banach Space ◽

Approximate Solution ◽

Integral Equations ◽

Kernel Methods ◽

Projection Methods ◽

Analytic Solutions ◽

Computational Method ◽

Fredholm Integral Equations ◽

Degenerate Kernel ◽

Quadrature Methods

This article is concerned with the construction of approximate analytic solutions to linear Fredholm integral equations of the second kind with general continuous kernels. A unified treatment of some classes of analytical and numerical classical methods, such as the Direct Computational Method (DCM), the Degenerate Kernel Methods (DKM), the Quadrature Methods (QM) and the Projection Methods (PM), is proposed. The problem is formulated as an abstract equation in a Banach space and a solution formula is derived. Then, several approximating schemes are discussed. In all cases, the method yields an explicit, albeit approximate, solution. Several examples are solved to illustrate the performance of the technique.

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Analysis of the Error in a Numerical Method Used to Solve Nonlinear Mixed Fredholm-Volterra-Hammerstein Integral Equations

Journal of Function Spaces and Applications ◽

10.1155/2012/242870 ◽

2012 ◽

Vol 2012 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

D. Gámez

Keyword(s):

Banach Space ◽

Integral Equation ◽

Approximate Solution ◽

Numerical Method ◽

Integral Equations ◽

Hammerstein Integral Equation ◽

Numerical Resolution ◽

Hammerstein Integral Equations ◽

Schauder Bases

This work presents an analysis of the error that is committed upon having obtained the approximate solution of the nonlinear Fredholm-Volterra-Hammerstein integral equation by means of a method for its numerical resolution. The main tools used in the study of the error are the properties of Schauder bases in a Banach space.

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