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Podlevskyi, B.M. (2012) Numerical Algorithms of Finding the Branching Lines and Bifurcation Points of Solutions for One Class of Nonlinear Integral Equations. In: Awrejcewicz, J. and Hagedorn, P., Eds., Nonlinearity, Bifurcation and Chaos: Theory and Applications, InTech Publishing, Novi Sad, 281-312.

has been cited by the following article:

• TITLE: The Radiation System Synthesis by the Power Criterion as a Problem of Optimization with Restrictions

  AUTHORS: Mykhaylo I. Andriychuk, Bohdan M. Podlevskyi

  KEYWORDS: Power RP, Variational Approach, Non-Linear Integral Equation, Successive Approximation Method

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.6 No.12, December 27, 2018

  ABSTRACT: A nonlinear synthesis problem of antennas according to the prescribed power (squared amplitude) radiation pattern (RP) is considered in the variational statement that yields in the possibility to take into account an additional restriction to the synthesized power RP. The problem of synthesis consists of finding such currents in antenna, which generates the RP with the best approximation to the given one. The respective Euler’s equation is reduced on the basis of used functional. This is nonlinear integral equation of Hammerstein’s type. The effective numerical methods are elaborated and applied for its solving. The computational results verify the effectiveness of approach proposed.