On the problem of restoring time coefficient-functions of special type source in parabolic equation

An inverse problem of identifying coefficients depend only on time for a special form source in a linear parabolic equation with point overdetermined conditions. In particular, boundary value problems with nonlocal (integral) boundary conditions are reduced to such problems. The specificity of the problems is that the identifiable parameters depend only on a time variable and are factors of the coefficients of the right-hand side of the equation. A method for numerically solving the problem using the method of lines is proposed, based on using a special type representation of solution. By applying the method of lines, the problem is reduced to a parametric inverse problem with respect to an ordinary differential equations system. For its solution, a special type of representation of this solution is proposed. To solve this problem, auxiliary boundary value problems are constructed that determine a solution to the initial problem. The most important in this work is that the proposed approach to the numerical solution to the investigated inverse problem of identifying the coefficients does not require (in contrast to previously known methods) to construct any iterative procedure. The results of numerical experiments in the form of tables and graphs obtained by solving the test problems, and their analysis are provided.