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One of the broad areas of research of computational mathematics is numerical solution of problems of mathematical physics with a curvilinear domain. One of the methods of solving such problems is finite difference method by using the fictitious domain. The fictitious domain method is a method of simplifying a geometrically complex original area by replacing the given area with a geometrically simple area, for example, a rectangle or parallelogram. In this method, the assumption is often made that the boundary condition on the fictitious boundary is equal to zero or is equal to the boundary condition on the original boundary. Thus, the fictitious domain method has the problem that the boundary condition at the original boundary is not satisfied due to an assumption. The subject of the presentation is updating this method by taking into account the boundary condition on the original boundary. For this purpose, the functional of the difference between the calculated and actual boundary condition is minimized using the adjoint equation.