ONE METHOD OF SOLVING LINEAR MULTIPARAMETER EIGENVALUE PROBLEM
V. V. KHLOBYSTOV
Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, 01601, Ukraine.
B. M. PODLEVSKYI *
Pidstryhach Institute of Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, 79030, Ukraine.
O. S. YAROSHKO
Faculty of Applied Mathematics and Informatics, Ivan Franko National University of Lviv, Lviv, 79000, Ukraine.
*Author to whom correspondence should be addressed.
Abstract
We consider a nonlinear multiparameter spectral problem in the real Euclidian space. In correspondence to this problem we put a variation problem on minimization of a specific functional. The equivalence of these two problems is proved. Beside that, based on a gradient procedure, we propose a numerical method for finding the eigenvalues and the eigenvectors of the spectral problem. Finally, we prove the convergence of this method and illustrate its application by several examples.
Keywords: Multiparameter eigenvalue problem, variation problem, iterative procedure