A Novel Mixed Method Using MM-SE with Change in Routhain Array for Model Order Reduction

The system modelling leads towards the higher-order differential equations. These systems are difficult to analyse. Therefore, for ease and understanding, the conversion of higher to lower order is required. The model order reduction(MOR) is a systematic procedure to tackle these kinds of situations. This paper offers a mixed method for MOR using the modified moment matching (MM) and stability equation (SE). The modification is applied in the routhain array of MM. The approach has been verified by examining the error between the original, proposed and compared with reduced order available in the literature. The obtained result has been compared on the basis of step response characteristics and the response indices error.

Some two-point boundary value problems for systems of higher order functional differential equations

In the paper we study the question of the solvability and unique solvability of systems of the higher order differential equations with the argument deviations \begin{equation*} u_i^{(m_i)}(t)=p_i(t)u_{i+1}(\tau _{i}(t))+ q_i(t), (i=\overline {1, n}), \text {for $t\in I:=[a, b]$}, \end{equation*} and \begin{equation*}u_i^{(m_i)} (t)=F_{i}(u)(t)+q_{0i}(t), (i = \overline {1, n}), \text {for $ t\in I$}, \end{equation*} under the conjugate $u_i^{(j_1-1)}(a)=a_{i j_1}$, $u_i^{(j_2-1)}(b)=b_{i j_2}$, $j_1=\overline {1, k_i}$, $j_2=\overline {1, m_i-k_i}$, $i=\overline {1, n}$, and the right-focal $u_i^{(j_1-1)}(a)=a_{i j_1}$, $u_i^{(j_2-1)}(b)=b_{i j_2}$, $j_1=\overline {1, k_i}$, $j_2=\overline {k_i+1,m_i}$, $i=\overline {1, n}$, boundary conditions, where $u_{n+1}=u_1, $ $n\geq 2, $ $m_i\geq 2, $ $p_i \in L_{\infty }(I; R), $ $q_i, q_{0i}\in L(I; R), $ $\tau _i\colon I\to I$ are the measurable functions, $F_i$ are the local Caratheodory's class operators, and $k_i$ is the integer part of the number $m_i/2$.In the paper are obtained the efficient sufficient conditions that guarantee the unique solvability of the linear problems and take into the account explicitly the effect of argument deviations, and on the basis of these results are proved new conditions of the solvability and unique solvability for the nonlinear problems.

CALCULATION OF PARAMETERS OF BRANCHED MECHANICAL SYSTEMS WITH HARMONIC VIBRATIONS. Continuation

Parallel-series and series-parallel connections of mechanical power consumers are considered. According to the known parameters of systems and the disturbing harmonic effect, the velocities of the elements of mechanical systems and the forces applied to them are algebraically determined. For the considered branched mechanical schemes, the classical methods based on solving second-order differential equations become many times more complicated and require solving systems of equations that reduce to higher-order differential equations. The use of a symbolic (complex) description of mechanical processes and systems makes it possible to use instead simple and compact algebraic methods, the complexity of which is ten times less. Vector diagrams, not being a necessary component of the study of mechanical systems, are of significant methodological importance, since they show quantitative and phase relationships between the parameters of systems.

Oscillation Results for Nonlinear Higher-Order Differential Equations with Delay Term

The aim of this work is to investigate the oscillation of solutions of higher-order nonlinear differential equations with a middle term. By using the integral averaging technique, Riccati transformation technique and comparison technique, several oscillatory properties are presented that unify the results obtained in the literature. Some examples are presented to demonstrate the main results.

Some Important Criteria for Oscillation of Non-Linear Differential Equations with Middle Term

In this work, we present new oscillation conditions for the oscillation of the higher-order differential equations with the middle term. We obtain some oscillation criteria by a comparison method with first-order equations. The obtained results extend and simplify known conditions in the literature. Furthermore, examining the validity of the proposed criteria is demonstrated via particular examples.

Reproducing kernel functions and homogenizing transforms

A lot of problems of the physical world can be modeled by non-linear ODE with their initial and boundary conditions. Especially higher order differential equations play a vital role in this process. The method for solution and its effectiveness are as important as the modelling. In this paper, on the basis of reproducing kernel theory, the reproducing kernel functions have been obtained for solving some non-linear higher order differential equations. Additionally, for each problem the homogenizing transforms have been obtained.

On some higher order equations admitting meromorphic solutions in a given domain

This paper relates to a recent trend in complex differential equations which studies solutions in a given domain. The classical settings in complex equations were widely studied for meromorphic solutions in the complex plane. For functions in the complex plane, we have a lot of results of general nature, in particular, the classical value distributions theory describing numbers of a-points. Many of these results do not work for functions in a given domain. A recent principle of derivatives permits us to study the numbers of Ahlfors simple islands for functions in a given domain; the islands play, to some extend, a role similar to that of the numbers of simple a-points. In this paper, we consider a large class of higher order differential equations admitting meromorphic solutions in a given domain. Applying the principle of derivatives, we get the upper bounds for the numbers of Ahlfors simple islands of similar solutions.