In this paper we present a finite element analysis for a Dirichlet boundary control problem where the Dirichlet control is considered in the energy space H1/2(Γ). As an equivalent norm in H1/2(Γ) we use a norm which is induced by a stabilized hypersingular boundary integral operator. The analysis is based on the mapping properties of the solution operators related to the primal and adjoint boun...

in this paper we consider a nonlinear two-phase stefan problem in one-dimensional space. the problem is mapped into a nonlinear volterra integral equation for the free boundary.

We deal with the general problem of scattering by open-arcs in two-dimensional space. We show that this problem can be solved by means of certain second-kind integral equations of the form Ñ S̃[φ] = f , where Ñ and S̃ are first-kind integral operators whose composition gives rise to a generalized Calderón formula of the form ÑS̃ = J̃τ 0 +K̃ in a weighted, periodized Sobolev space. (Here J̃τ 0 is a co...

In the first part of this work, we derive compact numerical quadrature formulas for finite-range integrals I [f ] = ∫ b a f (x) dx, where f (x)= g(x)|x − t |β , β being real. Depending on the value of β, these integrals are defined either in the regular sense or in the sense of Hadamard finite part. Assuming that g ∈ C∞[a, b], or g ∈ C∞(a, b) but can have arbitrary algebraic singularities at x ...

in this paper, a nonlinear volterra-fredholm integral equation of the first kind is solved by using the homotopy analysis method (ham). in this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by ham. the approximate solution of this equation is calculated in the form of a series which its components are computed easily. the accuracy...

in this paper, an iterative scheme for extracting approximate solutions of two dimensional volterra-fredholm integral equations is proposed. considering some conditions on the kernel of the integral equation obtained by discretization of the integral equation, the convergence of the approximate solution to the exact solution is investigated. several examples are provided to demonstrate the effc...

in this paper, we present a method for solving the rst kind abel integral equation. in thismethod, the rst kind abel integral equation is transformed to the second kind volterraintegral equation with a continuous kernel and a smooth deriving term expressed by weaklysingular integrals. by using sidi's sinm - transformation and modied navot-simpson'sintegration rule, an algorithm for...

In this paper, we propose and justify a spline-collocation method with first-order splines for approximate solution of nonlinear hypersingular integral equations Prandtl’s type. We obtained the estimates convergence rate error. The constructed computational scheme includes continuous solving operator equations, which is stable perturbations coefficients right-hand sides equations.

in this paper, existence theorems for the fuzzy volterra-fredholm integral equations of mixed type (fvfiemt) involving fuzzy number valued mappings have been investigated. then, by using banach's contraction principle, sufficient conditions for the existence of a unique solution of fvfiemt are given. finally, illustrative examples are presented to validate the obtained results.