An approach of finding the branching curves of nonlinear integral operator arising in the theory of antennas synthesis

Authors

  • B. M. Podlevskyi Institute of Applied Problems of Mechanics and Mathematics of NASU, Ukraine

DOI:

https://doi.org/10.1109/ICATT.2011.6170799

Abstract

In frameworks of simple mathematical model the nonlinear synthesis problem of a plane equidistant antenna array according to the given requirements to an amplitude directivity pattern is considered. When finding the branching curves of solutions of nonlinear integral equations, obtained as a result of solution of the synthesis problem, the two-parameter eigenvalue problems with spectral parameters analytically included in the kernel of the linearized integral operator arise. For such problems the numerical algorithm of finding the eigenvalue curves are considered. The numerical examples are presented.

References

ANDRIYCHUK, M.I.; VOITOVICH, N.N.; SAVENKO, P.O.; TKACHUK, V.P. The Antenna Synthesis According to Prescribed Amplitude Radiation Pattern: Numerical Methods and Algorithms. Kiev: Naukova Dumka, 1993 [in Russian].

VAINBERG, M.M.; TRENOGIN, V.A. Branching Theory of the Solution of Nonlinear Equations. Moscow: Nauka, 1969 [in Russian].

SAVENKO, P.O. Nonlinear Problems of Radiating Systems Synthesis (Theory and Methods of Solution). Lviv: IAPMM NASU, 2002 [in Ukraine].

PODLEVSKYI, B.M. On certain two-sided analogues of Newton's method for solving nonlinear eigenvalue problems. Comput. Math. Math. Physics, 2007, v.47, n.11, p.1745-1755.

PODLEVSKYI, B.M. On application of Newton's method to the determination of the eigenvalues of nonlinear spectral problems, Math. Methods and Physicomechanical Fields, 1997, v.40, n.1, p.146-150.

Published

2011-09-25