ANALYTICAL STUDY OF THE STATIC THERMOMECHANICAL STRESSES OF THE ASSEMBLIES WITH OPTIONAL RING FLANGES. ROTATION OF THE FLANGE RING AROUND THE CIRCUMFERENCE OF CENTERS FOR BOLT HOLE... by IATAN RADU I., GHEORGHITA TOMESCU, GEORGETA ROMAN (URSE), MELANIA CORLECIUC (MITUCA), IOLANDA CONSTANTA PANAIT

“…Regarding of the above, the compatibility of the deformations of the component elements (radial displacements and rotations) is approached. A linear algebraic system is formed in which both external loads (pressure, temperature) and connecting loads (bending unit moments and unit forces) are present. …”
Get full text

Numerical Solution for the 2D Linear Fredholm Functional Integral Equations by Neda Khaksari, Mahmoud Paripour, Nasrin Karamikabir

“…Using the proposed method, we get a system of linear algebraic equations which are solved by an iteration method. …”
Get full text

Numerical Solution of Time-Fractional Diffusion-Wave Equations via Chebyshev Wavelets Collocation Method by Fengying Zhou, Xiaoyong Xu

“…Based on the collocation technique, the second-kind Chebyshev wavelets are used to reduce the problem to the solution of a system of linear algebraic equations. Several examples are provided to confirm the reliability and effectiveness of the proposed method.…”
Get full text

Finite difference solution of radiation effects on MHD unsteady free-convection flow over vertical plate with variable surface temperature by M. A. Abd El-Naby, Elsayed M. E. Elbarbary, Nader Y. Abdelazem

“…The boundary layer equations are transformed into a linear algebraic system by an implicit finite-difference method. …”
Get full text

Bernoulli Collocation Method for Solving Linear Multidimensional Diffusion and Wave Equations with Dirichlet Boundary Conditions by Bashar Zogheib, Emran Tohidi, Stanford Shateyi

“…., CGL collocation points), equations will be transformed into the associated systems of linear algebraic equations which can be solved by robust Krylov subspace iterative methods such as GMRES. …”
Get full text

Construction Solutions of PDE in Parametric Form by Alexandra K. Volosova, Konstantin Alexandrovich Volosov

“…In the case of two independent variables 𝑥,𝑡, then it always gives the possibility of expressing all PDE second and more order as 𝐴𝑋=𝑏. This is a linear algebraic equations system with regards derivatives to old variables 𝑥(𝜉,𝛿), 𝑡(𝜉,𝛿) on new variables 𝜉,𝛿∶(𝑥′𝜉,𝑥′𝛿,𝑡′𝜉,𝑡′𝛿). …”
Get full text

Topology in nonlinear extensions of hypernumbers by M. S. Burgin

“…In this paper, nonlinear structures are introduced in spaces of real and complex hypernumbers by extending the concept of a hypernumber. In such a way, linear algebras of extended hypernumbers are built. A special topology of conical neighborhoods in these algebras is introduced and studied. …”
Get full text

Numerical method for solving the subdiffusion differential equation with nonlocal boundary conditions by Murat A. Sultanov, Vladimir E. Misilov, Makhmud A. Sadybekov

“…The Thomas algorithm was used to solve systems of linear algebraic equations. Numerical experiments were conducted to study the constructed algorithm. …”
Get full text

A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems by Yidu Yang, Wei Jiang, Yu Zhang, Wenjun Wang, Hai Bi

“…With this scheme, the solution of an eigenvalue problem on a fine grid Kh is reduced to the solution of an eigenvalue problem on a much coarser grid KH and the solution of a linear algebraic system on the fine grid Kh. Theoretical analysis shows that the scheme has high efficiency. …”
Get full text

Method of formation of numerical projection-grid algorithm on basis of «three-dimensional regular element» for calculation of 3D-models of magnetic field in cylindrical coordinate... by A. A. Tatevosyan, E. G. Andreeva

“…The use of the «three-dimensional regular element» makes it possible to automate the process of forming a global system of linear algebraic equations in the projection-grid Galerkin method in combination with the finite element method bypassing the stage of constructing elemental systems of equations. …”
Get full text

Approximate Solution of a Reduced-Type Index-k Hessenberg Differential-Algebraic Control System by Ghazwa F. Abd, Radhi A. Zaboon

“…The unknown coefficients of the solution are obtained by solving a linear algebraic system. The different index problems of linear Hessenberg differential-algebraic control systems are approximately solved using this approach with comparisons. …”
Get full text

Analytical solution of problem of shielding low-frequency magnetic field by thin-walled cylindrical screen in presence of cylinder by G. Ch. Shushkevich

“…It is shown that the solution of formulated boundary value problem is reduced to the solution of linear algebraic equations system for coefficients included in the representation of secondary fields. …”
Get full text

Modeling Current Distribution Within Conductors and Between Parallel Conductors in High-Frequency Magnetics by Michael Solomentsev, Alex J. Hanson

“…In this article, we show that Maxwell's equations, in the high frequency limit, yield a set of linear algebraic equations that are rapidly solvable to yield both the current and magnetic field distribution and hence can be used to predict loss and leakage inductance. …”
Get full text

Variationally Improved Bézier Surfaces with Shifted Knots by Daud Ahmad, Kanwal Hassan, M. Khalid Mahmood, Javaid Ali, Ilyas Khan, M. Fayz-Al-Asad

“…Instead of variational minimization of usual area functional, the quasi-minimal Bézier surface with shifted knots is obtained as the solution of variational minimization of Dirichlet functional that turns up as the sum of two integrals and the vanishing condition gives us the system of linear algebraic constraints on the control points. The coefficients of these control points bear symmetry for the pair of summation indices as well as for the pair of free indices. …”
Get full text

Free Vibration Analysis of Laminated Composite Double-Plate Structure System with Elastic Constraints Based on Improved Fourier Series Method by Ying Zhang, Dongyan Shi, Dongze He, Dong Shao

“…After that, a set of standard linear algebraic equations was obtained. On this basis, the natural frequency and mode shapes of the LCDPS can be obtained by solving the standard eigenvalue problem. …”
Get full text

Phase-lag mixed integral equation of a generalized symmetric potential kernel and its physical meanings in (3+1) dimensions by Azhar Rashad Jan

“…The degenerate method is employed to deduce the linear algebraic system (LAS). In addition, our endeavor yielded novel and distinct instances. …”
Get full text

FEATURES OF ELECTROMECHANICAL ACOUSTIC ENERGY CONVERSION BY CYLINDRICAL PIEZOCERAMIC TRANSDUCERS WITH INTERNAL SCREENS IN COMPOSITION OF FLAT SYSTEMS by A. G. Leiko, I. V. Kandrachuk, A. O. Sviatnenko

“…The physical fields arising from the emission of sound by such a system are determined by the joint solution of the system of differential equations: the wave equation; equations of motion of thin piezoceramic shells with circular polarization in displacements; the equations of forced electrostatics for piezoceramics at given boundary conditions, the conditions of conjugation of fields at the boundaries of the division of domains and electric conditions.The solution of the problem is reduced to the solution of an infinite system of linear algebraic equations with respect to unknown coefficients of field expansions.An analysis of the results of numerical calculations, performed on the basis of the obtained analytical relations, called to establish a number of features in the electromechanical acoustic transformation of energy by emitters in the composition of flat systems. …”
Get full text

PHYSICAL FIELDS OF CIRCULAR CYLINDRICAL PIEZOCERAMIC RECEIVER IN PRESENCE OF A FLAT ACOUSTIC SOFT SCREEN by A. V. Derepa, A. G. Leiko, O. N. Pozdniakova

“…The physical fields of the system under consideration were determined by following solutions: the wave equation; equations of motion of thin piezoceramic cylindrical shells in displacements; equations of stimulated electrostatics for piezoceramics for given boundary conditions, conditions for coupling fields at interfaces and electrical conditions.A general conclusion was made concerning solving of an infinite system of linear algebraic equations with respect to the unknown coefficients of the expansion of the fields. …”
Get full text

Accelerated Modeling of Transients in Electromagnetic Devices Based on Magnetoelectric Substitution Circuits by Sergii Tykhovod, Ihor Orlovskyi

“…This helps to transform integro-differential state equations into linear algebraic equations for the representations of the solution functions. …”
Get full text

First Basic Problem of Elasticity Theory for a Composite Layer with Two Thick-Walled Tubes by Oleksandr Yu. Denshchykov, Valentyn P. Pelykh, Yaroslav V. Hrebeniuk, Vitalii Yu. Miroshnikov

“…Satisfying the boundary conditions and conjugation conditions between the layer and the tubes, an infinite system of integro-algebraic equations is formed, which is reduced to linear algebraic equations of the second kind, and the reduction method is applied. …”