# Iterative method for the Dirichlet problem and its modifiations

### Abstract

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.

### References

*Mathematical notes of NEFU*, 24(3), pp. 38-51. doi: https://doi.org/10.25587/SVFU.2018.3.10888.

This work is licensed under a Creative Commons Attribution 4.0 International License.