We study the Fredholm minors associated with a Fredholm equation of the second type. We present a couple of new linear recursion relations involving the nth and n−1th minors, whose solution is a representation of the nth minor as an n × n determinant of resolvents. The latter is given a simple interpretation in terms of a path integral over non-interacting fermions. We also provide an explicit ...

This paper is concerned with weak solution of a mixed boundary value problem for the biharmonic equation in the plane. Using Green’s formula, the problem is converted into a system of Fredholm integral equations for the unknown data on different part of the boundary. Existence and uniqueness of the solutions of the system of boundary integral equations are established in appropriate Sobolev spa...

We study the Fredholm minors associated with a Fredholm equation of the second type. We present a couple of new linear recursion relations involving the nth and n−1th minors, whose solution is a representation of the nth minor as an n × n determinant of resolvents. The latter is given a simple interpretation in terms of a path integral over non-interacting fermions. We also provide an explicit ...

Abstract. Optimal control problems of forward-backward stochastic Volterra integral equations (FBSVIEs, in short) with closed control regions are formulated and studied. Instead of using spike variation method as one may imagine, here we turn to treat the non-convexity of the control regions by borrowing some tools in set-valued analysis and adapting them into our stochastic control systems. A ...

in this paper, we propose a successive approximation method based on fuzzy wavelet like operator to approximate the solution of linear fuzzy fredholm integral equations of the second kind with arbitrary kernels. we give the convergence conditions and an error estimate. also, we investigate the numerical stability of the computed values with respect to small perturbations in the first iteration....

in this paper, we present a new computational technique for solving nonlinear fredholm integral equations of the second kind. this proposed method is based on galerkin method and is computationally very attractive. moreover, for reducing the operations in comparing similar works, we design our algorithm based on transformations of orthogonal polynomials in approximation coefficients calculating...

A thin rigid plate is submerged beneath the free surface of deep water. The plate performs small-amplitude oscillations. The problem of calculating the radiated waves can be reduced to solving a hypersingular boundary integral equation. In the special case of a horizontal circular plate, this equation can be reduced further to onedimensional Fredholm integral equations of the second kind. If th...

M. A. Abdou, Khamis I. Mohamed and A. S. Ismail, On the numerical solutions of Fredholm-Volterra integral equation, Appl. Math. Comp. 146, 713-728, (2003). M. A. Abdou, Khamis I. Mohamed and A. S. Ismail, Toeplitz Matrix and product Nystrom methods for solving the singular integral equation, Le Matematiche LVII-Fasc. I, 21-37, (2002). H. Brunner, On the numerical solution of nonlinear VolterraF...

Orthogonal functions and polynomials have been used by many authors for solving various problems. The main idea of using orthogonal basis is that a problem reduces to solving a system of linear or nonlinear algebraic equations by truncated series of orthogonal basis functions for solution of problem and using the operational matrices. Here we use Legendre wavelets basis on interval [0, 1]. Some...