A certain inversion problem for the ray transform with incomplete data.
A conjecture of Gy. Petruska.
A direct method for boundary integral equations on a contour with a peak.
A factorization method for an inverse Neumann problem for harmonic vector fields.
A Liapunov functional for a linear integral equation.
A perturbed integral geometry problem in a three-dimensional space.
An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data
We propose an adaptive finite element method for the solution of a linear Fredholm integral equation of the first kind. We derive a posteriori error estimates in the functional to be minimized and in the regularized solution to this functional, and formulate corresponding adaptive algorithms. To do this we specify nonlinear results obtained earlier for the case of a linear bounded operator. Numerical experiments justify the efficiency of our a posteriori estimates applied both to the computationally...
An Adaptive Numerical Method for Solving Linear Fredholm Integral Equations of the First Kind.
An operational Haar wavelet method for solving fractional Volterra integral equations
A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the validity and applicability of the developed method.