ABSTRACT
The numerical-analytical methods used above for the construction of effective solutions of eigenvalue problems can be directly generalized to the case of multi-dimensional systems, more precisely, to eigenvalue problems for self-conjugate differential operators acting on vector-valued functions of a scalar argument. The differential operators may be of the second, the fourth, or a higher order. In particular, it is interesting to consider eigenvalue problems for coupled subsystems of Sturm-Liouville type. Next, we describe the procedure of the accelerated convergence method for a vector problem which cannot be split into sub-problems of smaller dimensions.
