Solution to classes of inverse coefficient problems and problems with nonlocal conditions for parabolic equations

We study the numerical solution to inverse problems in which one reconstructs the coefficients of a parabolic equation depending only on one (space or time) variable. In particular, these classes of problems arise in the study of boundary value problems with nonlocal (integral) boundary conditions. We suggest an approach to the numerical solution to these problems with the use of the line method and the reduction of the original problem to the solution to auxiliary Cauchy problems for systems of ordinary differential equations. We present the results of numerical experiments with test problems.