in this work, we present a computational method for solving second kindnonlinear fredholm volterra integral equations which is based on the use ofhaar wavelets. these functions together with the collocation method are thenutilized to reduce the fredholm volterra integral equations to the solution ofalgebraic equations. finally, we also give some numerical examples that showsvalidity and applica...

in this paper, we studied the numerical solution of nonlinear weakly singular volterra-fredholm integral equations by using the product integration method. also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear volterra-fredholm integral equations. the reliability and efficiency of the proposed scheme are...

2 Ep-Groupoids and Generalized Maps 17 2.1 Ep-Groupoids . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2 Functors and Equivalences . . . . . . . . . . . . . . . . . . . . 21 2.3 Inversion of Equivalences and Generalized Maps . . . . . . . . 28 2.4 Strong Bundles over Ep-Groupoids . . . . . . . . . . . . . . . 33 2.5 Auxiliary Norms . . . . . . . . . . . . . . . . . . . . . . . . . 4...

Recently, a beautiful identity due to Borodin and Okounkov was proved for Toeplitz determinants which shows how one can write a Toeplitz determinant as a Fredholm determinant. In this note we generalize this to the Wiener-Hopf case. The proof in the Wiener-Hopf case follows identically with the second one given in [1]. We include it here for completeness sake and because the nature of the ident...

Let A be a bounded operator on a separable, infinite dimensional Hilbert space H. Moreover, assume that A is not in the set C + K(H) of operators expressible as a sum of a scalar multiple of identity and a compact operator. What is the smallest similarity invariant semigroup containing operator A? Equivalently, which operators can be expressed as products of operators, similar to A? A partial a...

We prove that the operator G, the closure of the first-order differential operator −d/dt + D(t) on L2(R, X), is Fredholm if and only if the not well-posed equation u′(t) = D(t)u(t), t ∈ R, has exponential dichotomies on R+ and R− and the ranges of the dichotomy projections form a Fredholm pair; moreover, the index of this pair is equal to the Fredholm index of G. Here X is a Hilbert space, D(t)...

We study interfaces in an Allen-Cahn equation, separating two metastable states. Our focus is on a directional quenching scenario, where a parameter renders the system bistable in a half plane and monostable in its complement, with the region of bistability expanding at a fixed speed. We show that the growth mechanism selects a contact angle between the boundary of the region of bistability and...

We investigate the relationship between the decay at infinity of the right-hand side f and solutions u of an equation Lu = f when L is a second order elliptic operator on RN . It is shown that when L is Fredholm, u inherits the type of decay of f (for instance, exponential, or power-like). In particular, the generalized eigenfunctions associated with all the Fredholm eigenvalues of L, isolated ...

I n recent years, many numerical methods have been proposed for solving fuzzy linear integral equations. For example, in [10], the authors used the divided differences and finite differences methods for solving a parametric of the fuzzy Fredholm integral equations of the second kind. Also, in [9], a numerical method is proposed for the approximate solution of fuzzy linear Fredholm functional in...

We consider Dirichlet-to-Neumann maps associated with (not necessarily self-adjoint) Schrödinger operators in L2(Ω; dnx), where Ω ⊂ Rn, n = 2, 3, are open sets with a compact, nonempty boundary ∂Ω satisfying certain regularity conditions. As an application we describe a reduction of a certain ratio of modified Fredholm perturbation determinants associated with operators in L2(Ω; dnx) to modifie...