A new method for the numerical solution of nonlinear hyperbolic partial differential equations, describing wave phenomena especially in gas dynamics, is introduced. The nominated method belongs to the shock-capturing class and combines the ideas of mixed and anti-diffusion methods to establish a kind of mixed anti-diffusion method. It is based on the construction of difference schemes with second order of accuracy, which is total variation decreasing. The suggested schemes involve only three knots. The extension of the method to construct a few high accuracy difference schemes for elliptic and parabolic equations is also proposed. Numerical experiments, which illustrate the efficiency of the method, are carried out.