Product integration for weakly singular integral equations [PDF]
Mathematics of Computation, 1981 The product integration method is used for the numerical solution of weakly singular integral equations of the second kind. These equations often have solutions which have derivative singularities at the endpoints of the range of integration. Therefore, the order of convergence results of de Hoog and Weiss for smooth solutions do not hold in general ...
Claus Schneider
openaire +3 more sources
A note on the polynomial approximation of vertex singularities in the boundary element method in three dimensions [PDF]
, 2008 We study polynomial approximations of vertex singularities of the type $r^\lambda |\log r|^\beta$ on three-dimensional surfaces. The analysis focuses on the case when $\lambda > -\frac 12$.
Bespalov, A
core +7 more sources
An hp-version discontinuous Galerkin method for integro-differential equations of parabolic type [PDF]
, 2011 We study the numerical solution of a class of parabolic integro-differential equations with weakly singular kernels. We use an $hp$-version discontinuous Galerkin (DG) method for the discretization in time.
H. Mustapha +7 more
core +4 more sources
Localized direct segregated boundary-domain integral equations for variable-coefficient transmission problems with interface crack [PDF]
, 2011 The full text of the published article can be accessed at the link belowSome transmission problems for scalar second order elliptic partial differential equations are considered in a bounded composite domain consisting of adjacent anisotropic subdomains ...
Mikhailov, SE +2 more
core +6 more sources
Journal of Mathematics, 2022 In this paper, we establish several new weakly singular integral inequalities that generalize several previously known ones. Several applications for fractional differential equations in the Caputo context have been derived using tempered fractional ...
Abdellatif Ben Makhlouf +3 more
doaj +1 more source
Localized boundary-domain singular integral equations based on harmonic parametrix for divergence-form elliptic PDEs with variable matrix coefficients [PDF]
, 2013 This is the post-print version of the Article. The official publised version can be accessed from the links below. Copyright @ 2013 Springer BaselEmploying the localized integral potentials associated with the Laplace operator, the Dirichlet, Neumann and
Mikhailov, SE +2 more
core +1 more source
A new technical for solving a weakly singular integro-differential equations
Journal of Taibah University for Science, 2017 In this work, we transform a weakly singular integro-differential equations with logarithmic kernel to singular integral equations of Cauchy type and we prove by regularization the existence and uniqueness of the solution of this equations.
Mostefa Nadir
doaj +1 more source
Lagrangian flows for vector fields with gradient given by a singular integral [PDF]
, 2013 We prove quantitative estimates on ows of ordinary di erential equations with vector field with gradient given by a singular integral of an L1 function.
Crippa, Gianluca, Bouchut, Francois
core +1 more source
Flows of singular vector fields and applications to fluid and kinetic equations [PDF]
, 2015 Several physical phenomena arising in fluid dynamics and kinetic equations can be modeled by nonlinear transport PDE. Such quantities are the vorticity of a fluid, or the density of a collection of particles advected by a velocity field which is highly ...
Bohun, Anna
core +1 more source
A Regularization of Fredholm type singular integral equations
International Journal of Mathematics and Mathematical Sciences, 2001 We present a method to regularize first and second kind integral equations of Fredholm type with singular kernel. By appropriate application of the Poincaré-Bertrand formula we change such integral equations into a second kind Fredholm's integral ...
N. Aliev, S. Mohammad Hosseini
doaj +1 more source