—This paper is devoted to the construction of local approximations of functions of one and two variables using the polynomial, the trigonometric, and the exponential splines. These splines are useful for visualizing flows of graphic information. Here, we also discuss the parallelization of computations. Some attention is paid to obtaining two-sided estimates of the approximations using interval analysis methods. Particular attention is paid to solving the boundary value problem by using the polynomial splines and the trigonometric splines of the third and fourth order approximation. Using the considered splines, formulas for a numerical differentiation are constructed. These formulas are used to construct computational schemes for solving a parabolic problem. Questions of approximation and stability of the obtained schemes are considered. Numerical examples are presented.