Regularised discretisations obtained from first‐kind Fredholm operator equations
IET Microwaves, Antennas & Propagation, 2021 Judicious discretisations of certain first‐kind Fredholm operator equations are tantamount to Fredholm infinite‐matrix equations of the second kind. We give detailed explanations for the occurrence of this interesting and useful phenomenon and carefully ...
George Fikioris
doaj +1 more source
Integral reduction with Kira 2.0 and finite field methods [PDF]
Computer Physics Communications, 2020 We present the new version 2.0 of the Feynman integral reduction program Kira and describe the new features. The primary new feature is the reconstruction of the final coefficients in integration-by-parts reductions by means of finite field methods with ...
J. Klappert +3 more
semanticscholar +1 more source
On Nonlinear Integral Inequalities of Gronwall Type in Two Variables [PDF]
, 2003 In this paper we obtain some new nonlinear integral inequality of Gronwall type involving functions of two independent variables which can be used in the analysis of the behavior of the solutions of some partial differential ...
Kim, Young-Ho, Dragomir, Sever S
core +5 more sources
Functions of Positive and Negative Type, and their Connection with the Theory of Integral Equations
, 1909 The present memoir is the outcome of an attempt to obtain the conditions under which a given symmetric and continuous function k ( s, t ) is definite, in the sense of Hilbert.
James Mercer
semanticscholar +1 more source
Approximate solution of second kind integral equations on infinite cylindrical surfaces [PDF]
, 1994 The paper considers second kind integral equations of the form (abbreviated)φφK+=g, in which S is an infinite cylindrical surface of arbitrary smooth cross-section.
Peplow, AT, Chandler-Wilde, SN
core +5 more sources
Generalized Bihari Type Integral Inequalities and the Corresponding Integral Equations
Journal of Inequalities and Applications, 2009 We study some special nonlinear integral inequalities and the corresponding integral equations in measure spaces. They are significant generalizations of Bihari type integral inequalities and Volterra and Fredholm type integral equations.
László Horváth
doaj +2 more sources
A Unified Approach to Some Classes of Nonlinear Integral Equations
Journal of Function Spaces, 2014 We are going to discuss some important classes of nonlinear integral equations such as integral equations of Volterra-Chandrasekhar type, quadratic integral equations of fractional orders, nonlinear integral equations of Volterra-Wiener-Hopf type, and ...
Nurgali K. Ashirbayev +2 more
doaj +1 more source
Analysis of segregated boundary-domain integral equations for mixed variable-coefficient BVPs in exterior domains [PDF]
, 2011 This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2011 Birkhäuser Boston.Some direct segregated systems of boundary–domain integral equations (LBDIEs) associated with the mixed
Mikhailov, SE +5 more
core +1 more source
AN APPROXIMATE METHODS FOR SOLVING POLYSINGULAR INTEGRAL EQUATIONS IN DEGENERATE CASES
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2020 Background. This work is devoted to the study of sets of functions in which the condition of unique solvability of degenerate polysingular integral equations is satisfied, and to the construction of approximate methods for solving polysingular integral
I. V. Boykov +2 more
doaj +1 more source
Construction of Polynomial Lyapunov Functions Using Genetic Programming and Sparse Optimization
Journal of Optimization, Differential Equations and Their ApplicationsWe propose a hybrid evolutionary-sparse optimization framework for the automated synthesis of polynomial Lyapunov functions certifying exponential stability of nonlinear autonomous systems on a prescribed compact domain.
Valentyn V. Sobchuk +1 more
doaj +1 more source