V.M. ABDULLAYEV
APPROACH TO NUMERICAL SOLUTION TO COEFFICIENT-INVERSE PROBLEMS FOR PARABOLIC EQUATIONS
In the paper, we investigate numerical solution to coefficient inverse problems with respect to a parabolic type equation. We propose an approach to the solution to the considered problems, which is based on the use of the method of lines for reducing the initial problem to a system of ordinary differential equations with unknown parameters. Next we use a special representation of the solution to the derived boundary-value problem with respect to a linear system of differential equations with boundary conditions, with the help of which the parametric identification problem is reduced to the solution to auxiliary boundary-value problems and to a system of algebraic equations. We give the results of numerical experiments and carry out their analysis.
Keywords: inverse problem, method of lines, parabolic type equation, parametric identification
APPROACH TO NUMERICAL SOLUTION TO COEFFICIENT-INVERSE PROBLEMS FOR PARABOLIC EQUATIONS
In the paper, we investigate numerical solution to coefficient inverse problems with respect to a parabolic type equation. We propose an approach to the solution to the considered problems, which is based on the use of the method of lines for reducing the initial problem to a system of ordinary differential equations with unknown parameters. Next we use a special representation of the solution to the derived boundary-value problem with respect to a linear system of differential equations with boundary conditions, with the help of which the parametric identification problem is reduced to the solution to auxiliary boundary-value problems and to a system of algebraic equations. We give the results of numerical experiments and carry out their analysis.
Keywords: inverse problem, method of lines, parabolic type equation, parametric identification