Approximate Solution of the Inverse Boundary Value Problem for a Singularly Perturbed System of Partial Differential Equations

An initial–boundary value problem for a singularly perturbed system of partial differentialequations is considered. An inverse problem is formulated that consists in determining theunknown boundary condition based on one of the components of the solution given at a fixedpoint in space. Methods for the approximate solution of the inverse problem based on the use ofsmall parameter expansion of the solution of the initial–boundary value problem are proposed.Estimates of the accuracy of approximate solutions are obtained. The results of numericalcalculations illustrating the accuracy of the proposed methods are presented.