Iterative method for the Dirichlet problem and its modifications

A series of works of S. I. Kabanikhin's scientific school are devoted to study of the existence, uniqueness, and numerical methods for the inverse Dirichlet problem for the second-order hyperbolic equations. We consider a numerical solution to the non-classical Dirichlet problem and its modifications for the two-dimensional hyperbolic second-order equations. The method of iterative refinement of the missing initial condition is applied by means of an additional condition specified at the final time. Moreover, the direct problem is numerically realized at each iteration. The efficiency of the proposed computational algorithm is confirmed by calculations for two-dimensional model problems, including additional conditions with random errors.