We consider the problem of finding regularized solutions to ill-posed Volterra integral equations. The method we consider is a sequential form of Tikhonov regularization that is particularly suited to problems of Volterra type. We prove that when this sequential regularization method is coupled with several standard discretizations of the integral equation (collocation, rectangular and midpoint...

in this paper operational matrix of bernstein polynomials (bps) is used to solve bratu equation. this nonlinear equation appears in the particular elecotrospun nanofibers fabrication process framework. elecotrospun organic nanofibers have been used for a large variety of filtration applications such as in non-woven and filtration industries. by using operational matrix of fractional integration...

This paper describes a new numerical method for the solution of large linear discrete ill-posed problems, whose matrix is a Kronecker product. Problems of this kind arise, for instance, from the discretization of Fredholm integral equations of the first kind in two space-dimensions with a separable kernel. The available data (right-hand side) of many linear discrete ill-posed problems that aris...

Consider an operator equation F(u)=0 in a Hilbert space H and assume that this equation is solvable. Let us call the problem of solving this equation ill-posed if the operator F ′(u) is not boundedly invertible, and well-posed otherwise. A general method, Dynamical Systems Method (DSM), for solving linear and nonlinear illposed problems in H is presented. This method consists of the constructio...

Abstract In this paper, the heat conduction equation for composite materials posed and solved. The inverse Boundary Value Problem (BVP) described By studying solving direct problem in materials, we can determine function spaces solve problem. Sturm-Liouville method was used to by reduce it integral first kind. value be formulated as an kind equations. discretization algorithm applied reformulat...

We study well-posed perturbations of formally ill-posed diffusion equations which are used in image processing, such as the Perona–Malik equation. Our perturbation technique is to consider the diffusion equations as L gradient flows on integral functionals and then modify the inner product from L to a Sobolev inner product. We show that the functional differential equations obtained in this way...