ИСТИНА

In this work we are considering some inverse problem for a singular perturbed reaction-advection-diffusion equation. This problem is ill-posed and for its solution a regularizing algorithm has to be constructed in order to stabilise the approximate solution (for example, it could be the Tikhonov regularization that uses minimizing of corresponding regularizing functional). It is well known that it is impossible to construct stable methods for an ill-posed problem without knowledge of errors of the input data and errors of the approximate solution of the direct problem that has to be solved on each step of the minimizing procedure of the regularizing functional. Several recent results will be presented on the study of the above mentioned problem of error estimation for the approximate solution of the singular perturbed reaction-advection-diffusion equation. We propose new algorithm that would help us to perform a posteriory error estimation of the approximate solution based on implementation of 1) method of lines that reduces the initial partial differential equation to the stiff system of ordinary differential equations, 2) very stable Rosenbrock scheme with complex coefficient for stiff system of ordinary differential equations, 3) the Richardson extrapolation, 3) a dynamic adaptive mesh that preserve the order of accuracy of the Rosenbrock scheme that give us the opportunity to use the Richardson extrapolation for a posteriory error estimation.