Numerical Solutions of Integral Equations on the Half Line. I. The Compact Case.
On a Class of Fractional Type Integral Equations in Variable Exponent Spaces
2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30We obtain a criterion of Fredholmness and formula for the Fredholm index of a certain class of one-dimensional integral operators M with a weak singularity in the kernel, from the variable exponent Lebesgue space L^p(·) ([a, b], ?) to the Sobolev type space L^α,p(·) ([a, b], ?) of fractional smoothness. We also give formulas of closed form solutions ϕ ∈ L^p(·) of the 1st kind integral equation M0ϕ = f, known as the generalized...
On a class of multivalued variational inequalities.
On a generalized Wiener-Hopf integral equation
Let be such that . In this note we use the Mittag-Leffler partial fractions expansion for to obtain a solution of a Wiener-Hopf integral equation.
On a singular integral equation with log kernel and its application.
On optimal regularization methods for fractional differentiation.
On quadrature methods for the double layer potential equation over the boundary of a polyhedron.
On the Convergence of Multi-Grid Methods for a Hypersingular Integral Equation of the First Kind.
On the Convergence of the Galerkin Method for Nonsmooth Solutions of Integral Equations.
On the efficient use of the Galerkin-method to solve Fredholm integral equations
In the present paper we describe, how to use the Galerkin-method efficiently in solving boundary integral equations. In the first part we show how the elements of the system matrix can be computed in a reasonable time by using suitable coordinate transformations. These techniques can be applied to a wide class of integral equations (including hypersingular kernels) on piecewise smooth surfaces in 3-D, approximated by spline functions of arbitrary degree. In the second part we show, how to use the...
On the existence and uniqueness of non-negative solutions of a certain non-linear convolution equation
On the Fourier cosine—Kontorovich-Lebedev generalized convolution transforms
We deal with several classes of integral transformations of the form where is an operator. In case is the identity operator, we obtain several operator properties on with weights for a generalized operator related to the Fourier cosine and the Kontorovich-Lebedev integral transforms. For a class of differential operators of infinite order, we prove the unitary property of these transforms on and define the inversion formula. Further, for an other class of differential operators of finite...
On the Numerical Resolution of the Generalized Airfoil Equation with Possio Kernel.
On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation.
On the numerical solution of an Abel integral equation
On the numerical solution of the generalized Abel integral equation
On the numerical solution of the multidimensional singular integrals and integral equations, used in the theory of linear viscoelasticity.
On the polyconvolution with the weight function for the Fourier cosine, Fourier sine, and the Kontorovich-Lebedev integral transforms.
On the solution of an integral equation appearing in displacement problems.
On the solution of distributional Abel integral equation by distributional Sumudu transform.