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Even though the research style of algebra and analysis are quite different, many algebraic structures naturally arose from analysis, differential equations and integral equations, inspiring further ap...
In this talk, I will describe a moving sphere approach to a class of integral equations with bubble-type kernel. This class of equations comes from higher-order elliptic equations on the standard sphe...
We consider elliptic and parabolic variational equations and inequalities governed by integro-differential operators of order 2s ∈ (0,2]. Our main motivation is the pricing of European or Amer...
An iteration method is described to solve one-dimensional, first-kind integral equations with finite integration limits and difference kernel, K(x − x), that decays exponentially. The method re...
This article reviews several fast algorithms for boundary integral equations. After a brief introduction of the boundary integral equations for the Laplace and Helmholtz equations, we discuss in order...
A Fredholm second kind integral equation (SKIE) formulation is constructed for the Dirichlet problem of the biharmonic equation in three dimensions. A fast numerical algorithm is developed based on th...
This paper introduces the hierarchical interpolative factorization for integral equations (HIF-IE) associated with elliptic problems in two and three dimensions.This factorization takes the form of an...
In this paper we propose a convergence acceleration method for collocation solutions of the linear second-kind Volterra integral equations with proportional delay qt (0 < q < 1). This convergence a...
In this paper, we apply the modified Adomian Decomposition Method to get the numerical solutions of Quadratic integral equations. The appearance of noise terms in Decomposition Method was investigated...
In this article, we use scaling function interpolation method to solve linear Fredholm integral equations, and we prove a convergence theorem for the solution of Fredholm integral equations. We presen...
In this work, we prove a generalization of Osgood’s test for the ex-plosion of the solutions of initial-value problems. We also establish a comparison criterion for the solution of integral equations ...
It is shown in this paper that there is a connection between the Riemann zeta-function $\zf$ and the Bessel's functions. In this direction, a new class of the nonlinear integral equations is introduce...
In this paper, we deal with a class of backward doubly stochastic differential equations (BDSDEs, in short) involving subdifferential operator of a convex function and driven by Teugels martingales a...
For weighted Toeplitz operators T N ' defined on spaces of holomorphic functions in the unit ball, we derive regularity prop-erties of the solutions f to the integral equation T N ' (f) = h in terms o...
This paper formulates and studies a stochastic maximum principle for forward-backward stochastic Volterra integral equations (FBSVIEs in short), while the control area is assumed to be convex. Then a ...

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