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Haar wavelets method for solving Pocklington's integral equation

M. Shamsi, Mohsen Razzaghi, J. Nazarzadeh, Masoud Shafiee (2004)

Kybernetika

A simple and effective method based on Haar wavelets is proposed for the solution of Pocklington’s integral equation. The properties of Haar wavelets are first given. These wavelets are utilized to reduce the solution of Pocklington’s integral equation to the solution of algebraic equations. In order to save memory and computation time, we apply a threshold procedure to obtain sparse algebraic equations. Through numerical examples, performance of the present method is investigated concerning the...

Hammerstein equations with an integral over a noncompact domain

Robert Stańczy (1998)

Annales Polonici Mathematici

The existence of solutions of Hammerstein equations in the space of bounded and continuous functions is proved. It is obtained by the Schauder fixed point theorem using a compactness theorem. The result is applied to Wiener-Hopf equations and to ODE's.

Hammerstein–Nemytskii Type Nonlinear Integral Equations on Half-line in Space L 1 ( 0 , + ∞ ) ∩ L ∞ ( 0 , + ∞ )

Aghavard Kh. Khachatryan, Khachatur A. Khachatryan (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The paper studies a construction of nontrivial solution for a class of Hammerstein–Nemytskii type nonlinear integral equations on half-line with noncompact Hammerstein integral operator, which belongs to space L 1 ( 0 , + ∞ ) ∩ L ∞ ( 0 , + ∞ ) . This class of equations is the natural generalization of Wiener-Hopf type conservative integral equations. Examples are given to illustrate the results. For one type of considering equations continuity and uniqueness of the solution is established.

Hilbert transforms and the Cauchy integral in euclidean space

Andreas Axelsson, Kit Ian Kou, Tao Qian (2009)

Studia Mathematica

We generalize the notions of harmonic conjugate functions and Hilbert transforms to higher-dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These harmonic conjugates are in general far from being unique, but under suitable boundary conditions we prove existence and uniqueness of conjugates. The proof also yields invertibility results for a new class of generalized double layer potential operators on Lipschitz surfaces and boundedness of related Hilbert...

Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations

Guy Barles, Emmanuel Chasseigne, Cyril Imbert (2011)

Journal of the European Mathematical Society

This paper is concerned with the Hölder regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain, either the equation is strictly elliptic in the classical fully non-linear sense, or (and this is the most original part of our work) the equation is strictly elliptic in a non-local non-linear sense we make precise. Next we impose some regularity and growth...

Hypersingular integral equations and applications to porous elastic materials with periodic cracks

Michele Ciarletta, Gerardo Iovane (2005)

Bollettino dell'Unione Matematica Italiana

In this work a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions, is presented. The first goal of the present study is the development of an efficient analytical and direct numerical collocation method. The second one is the application of the method to the porous elastic materials when a periodic array of co-planar cracks is present. Starting from Cowin- Nunziato model...

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