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.
Integral equations of the third kind
Integral Equations VIA Saddle Point Problem for 2D Electromagnetic Problems
A new system of integral equations for the exterior 2D time harmonic scattering problem is investigated. This system was first proposed by B. Després in [11]. Two new derivations of this system are given: one from elementary manipulations of classical equations, the other based on a minimization of a quadratic functional. Numerical issues are addressed to investigate the potential of the method.
Integral Equations with Transform Kernels and the Eigenproblem KCx = ...x.
Iterative Berechnung mehrfacher Lösungen von Hammersteinschen Integralgleichungen.
Iterative sinc-convolution method for solving radiosity equation in computer graphics.
Iterative Variants of the Nyström Method for the Numerical Solution of Integral Equations.