The paper is devoted to the problem of construction of value functions in optimal control problems on infinite horizon for economic growth models. Grid approximation schemes for stationary Hamilton-Jacobi equations are realized for numerical calculation of value functions and optimal controls. For compactification of the grid domain and the range of the value function a series of nonlinear changes of variables are implemented for generating the contraction-mapping operators in the convergent approximation schemes. A special sample of economic growth model is used for verification of calculation results for value functions and optimal controls in grid approximation schemes.