‎‎‎‎‎‎‎‎‎‎‎‎‎This paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and product‎. ‎The main aim is to generalize the Jacobi integral and product operational matrices to the solving system of Fredholm and Volterra integro--differential equations‎ which appear in various fields of science such as physics and engineering. ‎The Operational matr...

The integral equation method is widely used for solving many problems in mathematical physics and engineering. This article proposes a computational method for solving nonlinear Fredholm-Volterra integral equations. Several numerical methods for approximating the solution of linear and nonlinear integral equations and specially FredholmVolterra integral equations are known [1-10]. Also, BlockPu...

Surjectivity results of Fredholm alternative type are obtained for nonlinear operator equations of the form λT (x)−S(x) = f , where T is invertible, and T, S satisfy various types of homogeneity conditions. We are able to answer some questions left open by Fuč́ık, Nečas, Souček, and Souček. We employ the concept of an a-stably-solvable operator, related to nonlinear spectral theory methodology. ...

In this paper, we present a novel approach to solve nonlinear Fredholm integral equations of the second kind. This algorithm is constructed by the integral mean value theorem and Newton iteration. Convergence and error analysis of the numerical solutions are given. Moreover, Numerical examples show the algorithm is very effective and simple.

Compactly supported linear semiorthogonal B-spline wavelets together with their dual wavelets are developed to approximate the solutions of nonlinear Fredholm-Hammerstein integral equations. Properties of these wavelets are first presented; these properties are then utilized to reduce the computation of integral equations to some algebraic equations. The method is computationally attractive, an...

We study the absolute continuity of the image measure of the canonical Poisson probability measure under nonlinear shifts. The Radon-Nykodim density function is expressed using a Carleman-Fredholm determinant and a divergence operator. Results are obtained for non-necessarily invertible transformations, under almost-sure differentiability hypothesis.

The parameter imbedding method for the Fredholm equation converts it into an initial value problem in its parameter λ. We establish the method for general operator equations of the form [I + ˆ f (λ)]ψ = φ. It is particularly useful for studying spontaneous symmetry breaking problems, such as contained in the nonlinear Schwinger-Dyson equation.

Integral equations of mixed Voltera-Fredholm type arise in various physical and biological problems. In the present paper, we obtain the approximate solution of the nonlinear Volterra-Hammerstein integral equations of mixed type in terms of Taylor polynomial. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments.

In this work, a computational method for solving nonlinear Volterra-Fredholm-Hammerestein integral equations is proposed. Compactly supported semiorthogonal cubic B-spline wavelets are employed as basis functions then collocation method is utilized to reduce the computation of integral equations to some algebraic system. The method is computationally attractive, and applications are demonstrate...

We study the J−holomorphic curves in the symplectization of the contact manifolds and prove that there exists at least one periodic Reeb orbits in any closed contact manifold with any contact form by using the well-known Gromov's nonlinear Fredholm alternative for J−holomorphic curves. As a corollary, we give a complete solution on the well-known Weinstein conjecture.