Error solving the wave equation based on the scheme with weights

Investigations have been fulfilled of wave equation approximation based on weighted difference scheme. For this purpose analytical solution has been built for semi-discretization case, when the difference spatial derivatives have been used for appropriate continuous derivatives approximation and system of second order differential equations with continuous time variable has been obtained. The analytical solution problem has been constructed for initial value problem for this system, using orthogonal system of eigenvectors for the second order difference derivatives in the spatial variables. It has been allowed to investigate approximation error, stability and to define optimal values of the weighting parameter at first for the best accuracy (of 4-th order for time step) and at second — for minimizing error for the values of the oscillation frequency for difference wave equation in comparison of continuous wave equation.