Numerical Identification of the Dependence of the Right Side of the Wave Equation on the Spatial Variable

The problem of identifying the multiplier of the right side of a one-dimensional wave equation depending on a spatial variable is considered. As additional information, the condition of the final redefinition is set. A discrete analogue of the inverse problem is constructed using the finite difference method. To solve the resulting difference problem, a special representation is proposed, with the help of which the difference problem splits into two independent difference problems. As a result, an explicit formula is obtained for determining the approximate value of the desired function for each discrete value of a spatial variable. The presented results of numerical experiments conducted for model problems demonstrate the effectiveness of the proposed computational algorithm.