Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170) proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems. However, in many applied problems, operators appear that do not satisfy these requirements, e.g. Helmholtz-type operators. Therefore, in this study, an alternating procedure for solving Cauchy problems for self-adjoint non-coercive elliptic operators of second order is presented. A convergence proof of this procedure is given.
- Cauchy problem
- Helmholtz equation
Johansson, B. T., & Kozlov, V. A. (2009). An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium. IMA Journal of Applied Mathematics, 74(1), 62-73. https://doi.org/10.1093/imamat/hxn013