Finite-part singular integral approximations in Hilbert spaces.
First kind integral equations for the numerical solution of the plane Dirichlet problem
We present, in a uniform manner, several integral equations of the first kind for the solution of the two-dimensional interior Dirichlet boundary value problem. We apply a general numerical collocation method to the various equations, and thereby we compare the various integral equations, and recommend two of them. We give a survey of the various numerical methods, and present a simple method for the numerical solution of the recommended integral equations.
Fonctionnelle quadratique et équations intégrales pour les problèmes d'onde harmonique en domaine extérieur
Fourier approximation for integral equations on the real line.
Fourier method for Laplace transform inversion.
Fourier Reconstruction in Tomography.
From classical numerical mathematics to scientific computing.
Fully Discrete Galerkin Approximations of Parabolic Boundary-Value Problems with Nonsmooth Boundary Data.
Galerkin methods for multidimensional nonlinear Volterra type equations
Galerkin methods for nonlinear Volterra type equations
Galerkin Methods with Splines for Singular Integral Equations over (0, 1).
Gaussian direct quadrature methods for double delay Volterra integral equations.
Global error estimation in the numerical solution of integro-differential equations by Euler's method
Haar wavelets method for solving Pocklington's integral equation
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...
High accuracy combination method for solving the systems of nonlinear Volterra integral and integro-differential equations with weakly singular kernels of the second kind.
High frequency approximation of integral equations modeling scattering phenomena
Homogenization of the criticality spectral equation in neutron transport
Homogenization of the criticality spectral equation in neutron transport
We address the homogenization of an eigenvalue problem for the neutron transport equation in a periodic heterogeneous domain, modeling the criticality study of nuclear reactor cores. We prove that the neutron flux, corresponding to the first and unique positive eigenvector, can be factorized in the product of two terms, up to a remainder which goes strongly to zero with the period. One term is the first eigenvector of the transport equation in the periodicity cell. The other term is the...
Implicit Runge- Kutta Methods for Second Kind Volterra Integral Equations.
Improving the Accuracy of Collocation Solutions of Volterra Integral Equations of the First Kind by Local Interpolation.