Numerical solution to parametric identification problems for partial differential equations

The paper proposes a numerical method for solving the problem, based on the use of the method of lines to reduce the problem to a system of ordinary differential equations with unknown parameters. Next, we use a special representation of the solution of the obtained boundary value problem for a linear system of differential equations with nonlocal conditions, by means of which the problem of parametric identification reduces to solving auxiliary boundary value problems and a system of algebraic equations. It is important to note that, unlike optimization approaches, The construction of any iterative procedures or minimizing sequences is used.