نتایج جستجو برای: singular integral equation

تعداد نتایج: 379015  

2012
A. G. Ramm

Inverse scattering problem is discussed for the Maxwell’s equations. A reduction of the Maxwell’s system to a new Fredholm second-kind integral equation with a scalar weakly singular kernel is given for electromagnetic (EM) wave scattering. This equation allows one to derive a formula for the scattering amplitude in which only a scalar function is present. If this function is small (an assumpti...

2006
T. D. Browning R. Dietmann

Let n 4, and let Q ∈ Z[X1,. .. , Xn] be a non-singular quadratic form. When Q is indefinite we provide new upper bounds for the least non-trivial integral solution to the equation Q = 0, and when Q is positive definite we provide improved upper bounds for the least positive integer k for which the equation Q = k is insoluble in integers, despite being soluble modulo every prime power.

1997
C. Dalitz E H. de Groot

An explicit solution of the stationary one dimensional half-space boundary value problem for the linear Boltzmann equation is presented in the presence of an arbitrarily high constant external field. The collision kernel is assumed to be separable, which is also known as “relaxation time approximation”; the relaxation time may depend on the electron velocity. Our method consists in a transforma...

2006
T. D. BROWNING

Let n > 4, and let Q ∈ Z[X1, . . . , Xn] be a non-singular quadratic form. When Q is indefinite we provide new upper bounds for the least non-trivial integral solution to the equation Q = 0, and when Q is positive definite we provide improved upper bounds for the greatest positive integer k for which the equation Q = k is insoluble in integers, despite being soluble modulo every prime power.

Journal: :The Computer Science Journal of Moldova 2000
Tudor Cibotaru

We investigate in this paper problems of theoretical foundation of collocations and mechanical quadratures methods for approximate solution of singular integral equation systems in the case, when their symbols have on the integration contour a finite set of integer degree zeroes. We consider the case when equation digitalization points are taken in such a way that each point of the contour can ...

2010
Hermann Brunner HERMANN BRUNNER

Since the solution of a second-kind Volterra integral equation with weakly singular kernel has, in general, unbounded derivatives at the left endpoint of the interval of integration, its numerical solution by polynomial spline collocation on uniform meshes will lead to poor convergence rates. In this paper we investigate the convergence rates with respect to graded meshes, and we discuss the pr...

Journal: :Physical review. E, Statistical, nonlinear, and soft matter physics 2001
A Tang J W Norbury

A method is presented for solving the momentum-space Schrödinger equation with a linear potential. The Lande-subtracted momentum-space integral equation can be transformed into a matrix equation by the Nystrom method. The method produces only approximate eigenvalues in the cases of singular potentials such as the linear potential. The eigenvalues generated by the Nystrom method can be improved ...

2003
Benjamin Jourdain Sylvie Méléard Wojbor A. Woyczynski

We consider a class of nonlinear integro-differential equations involving a fractional power of the Laplacian and a nonlocal quadratic nonlinearity represented by a singular integral operator. Initially, we introduce cut-off versions of this equation, replacing the singular operator by its Lipschitz continuous regularizations. In both cases we show the local existence and global uniqueness in L...

2002
Yijun Liu

A weakly singular form of the hypersingular boundary integral equation (BIE) (traction equation) for 3-D elastic wave problems is developed in this paper. All integrals involved are at most weakly singular and except for a stronger smoothness requirement on boundary elements, regular quadrature and collocation procedures used for conventional BIEs are sufficient for the discretization of the or...

پایان نامه :وزارت علوم، تحقیقات و فناوری - دانشگاه تربیت دبیر شهید رجایی 1390

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