Mykhaylo Andriychuk

Pidstryhach Institute for Applied Problems of Mechanics and Mathematics Ukraine

Prof. Mykhaylo Andriychuk obtained an M.Sc. degree in computational mathematics from the Lviv National University, a Ph.D. degree in the application of computational techniques from the Kyiv National University, and a D.Sc. degree in mathematical modeling from the Lviv Polytechnic National University in 1976, 1987, and 2015, respectively. He is now with the Pidstryhach Institute for Applied Problems of Mechanics and Mathematics (IAPMM), Lviv, Ukraine. Currently, he is the Head of Department of the Numerical Methods in Mathematical Physics at the IAPMM. His professional performance includes more than 180 papers in scientific journals and international conference proceedings, which concern diffraction and antenna synthesis theory, optimization methods, and nonlinear integral and matrix equations. He is the author of three monographs related to antenna theory. IEEE M’95, SM’03.

2books edited

3chapters authored

Latest work with IntechOpen by Mykhaylo Andriychuk

Matrix Theory - Classics and Advances examines matrix theory and its application in solving a series of problems related to natural phenomena and applied science. It consists of eleven chapters divided into two sections. Section 1, “Theory and Progress”, discusses the classical problems of matrix theory and its contribution to different fields of pure mathematics. Section 2, “Applications”, contains the research related to the application of matrix theory in applied science.

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Matrix Theory

Edited by Mykhaylo Andriychuk

Books edited

Numerical Simulation

Edited by Mykhaylo Andriychuk

Chapters authored

Numerical Solution of Many-Body Wave Scattering Problem for Small Particles and Creating Materials with Desired Refraction Coefficient

By M. I. Andriychuk and A. G. Ramm

Part of the book: Numerical Simulations of Physical and Engineering Processes

Synthesis of Antenna Systems According to the Desired Amplitude Radiation Characteristics

By Mykhaylo Andriychuk

Part of the book: Numerical Simulation

Advanced Methods for Solving Nonlinear Eigenvalue Problems of Generalized Phase Optimization

By Mykhaylo Andriychuk

In the process of solving the problems of generalized phase optimization the necessity to apply an eigenvalue approach often appears. The practical statement of the optimization problems consists of using the amplitude characteristics of functions that are sought. The usual way of optimization is deriving the Euler equation of the functional, which is used as criterion of optimization. As a rule, such equation is an integral one. It is worth pointing out that the integral equations of the generalized phase optimization are nonlinear ones. The characteristic property of such equations is non-uniqueness of solutions and their branching or bifurcation. The determination of branching solutions leads to the investigation of the corresponding homogeneous equations and the respective eigenvalue problem. This problem is nonlinear because of specificity of the statement of the optimization problem. The study of the above problem allows us to determine a set of points, in which the respective eigenvalues are equal to unity that determines the branching points of solutions. The data of calculations testify to the ability of the approach proposed to determine the solutions of nonlinear equations numerically with not large computations.

Part of the book: Matrix Theory

Mykhaylo Andriychuk

Latest work with IntechOpen by Mykhaylo Andriychuk

Matrix Theory

Books edited

Numerical Simulation

Chapters authored

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