Application of Müntz Orthogonal Functions on the Solution of the Fractional Bagley–Torvik Equation Using Collocation Method with Error Stimate by S. Akhlaghi, M. Tavassoli Kajani, M. Allame

“…By using the Riemann–Liouville fractional integral operator that we define for the Müntz orthogonal functions, the process of numerically solving the fractional Bagley–Torvik equation that is solved using Müntz orthogonal functions is reduced, and finally, we reach a system of algebraic equations. By solving algebraic equations and obtaining the vector of unknowns, the fractional Bagley–Torvik equation is solved using Müntz orthogonal functions, and the error value of the method can be calculated. …”
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Mathematical Model and Characteristics of the Induction Motor with a Power Supply from a Current Source by V. S. Malyar, A. V. Malyar

“…The non-linear system of algebraic equations of electrical equilibrium describing the steady-state modes is solved by the parameter continuation method. …”
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A SYNTHESIS METHOD OF BASIC TERNARY BENT-SQUARES BASED ON THE TRIAD SHIFT OPERATOR by O. N. Zhdanov, A. V. Sokolov

“…Practical application of advanced algebraic constructions in modern communication systems based on MC-CDMA (Multi Code Code Division Multiple Access) technology and in cryptography necessitates their further research. …”
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ESTABLISHED MODES AND STATIC CHARACTERISTICS OF THREE-PHASE ASYNCHRONOUS MOTOR POWERED WITH SINGLE PHASE NETWORK by V. S. Malyar, V. V. Malyar

“…The resulting nonlinear system of algebraic equations is a discrete analogue of the initial system of differential equations. …”
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Quasi-discreted dynamics of a neural net: The lighthouse model by Hermann Haken

“…Because of the δ-functions, the phase-equations can be converted into algebraic equations at discrete times. We first exemplify our procedure by two neurons, and then present the results for N neurons. …”
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A New Optimized Runge-Kutta Pair for the Numerical Solution of the Radial Schrödinger Equation by Yonglei Fang, Qinghong Li, Qinghe Ming, Kaimin Wang

“…The two RK methods in the pair have algebraic orders five and four, respectively. The two methods of the embedded pair are derived by nullifying the phase lag, the first derivative of the phase lag of the fifth-order method, and the phase lag of the fourth-order method. …”
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Note on the Solution of Transport Equation by Tau Method and Walsh Functions by Abdelouahab Kadem, Adem Kilicman

“…The main characteristic of this technique is that it reduces the problems to those of solving a system of algebraic equations; thus, it is greatly simplifying the problem.…”
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Exponential Collocation Method for Solutions of Singularly Perturbed Delay Differential Equations by Şuayip Yüzbaşı, Mehmet Sezer

“…By aid of the collocation points and the matrix operations, the suggested scheme converts singularly perturbed problem into a matrix equation, and this matrix equation corresponds to a system of linear algebraic equations. Also, an error analysis technique based on the residual function is introduced for the method. …”
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On the Deformations and Derivations of n-Ary Multiplicative Hom-Nambu-Lie Superalgebras by Baoling Guan, Liangyun Chen, Yao Ma

“…As a generalization of the notion of derivations for n-ary multiplicative Hom-Nambu-Lie algebras, we discuss the derivations of n-ary multiplicative Hom-Nambu-Lie superalgebras. …”
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Inversion Free Algorithms for Computing the Principal Square Root of a Matrix by Nicholas Assimakis, Maria Adam

“…It is certified that the proposed algorithms are equivalent to the classical Newton method. An inversion free algebraic method, which is based on applying the Bernoulli substitution to a special case of the continuous time Riccati equation, is also proposed.…”
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Nonlinear asymptotic stability in $L^\infty $ for Lipschitz solutions to scalar conservation laws by Golding, William

“…As an application, we are able to compute algebraic decay rates of the $L^\infty $ norm of perturbations of global-in-time Lipschitz solutions, including perturbations of planar rarefaction waves. …”
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Polynomial Reproduction of Vector Subdivision Schemes by Y. F. Shen, D. H. Yuan, S. Z. Yang

“…We first present a simple algebraic condition for polynomial reproduction of such schemes with standard subdivision symbol. …”
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Weakly 2-Absorbing Ideals in Almost Distributive Lattices by Natnael Teshale Amare

“…The concepts of weakly 2-absorbing ideal and weakly 1-absorbing prime ideal in an almost distributive lattice (ADL) are introduced, and the necessary conditions for a weakly 1-absorbing prime ideal to become a weakly 2-absorbing ideal in algebraic form are proved. Also, weakly 2-absorbing ideals are characterized in terms of weakly prime ideals and 2-absorbing ideals. …”
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Three-Dimensional Expansion and Graphical Concept of Generalized Triangular Fuzzy Set by Yong Sik Yun

“…We have studied the extended algebraic operations between two fuzzy numbers and calculated Zadeh’s max-min composition operator for two generalized triangular fuzzy sets in ℝ2. …”
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Modeling the daily activities of breeding colonial seabirds: Dynamic occupancy patterns in multiple habitat patches by Andrea L. Moore, Smruti P. Damania, Shandelle M. Henson, James L. Hayward

“…We used timescale techniques to reduce the differential equations to algebraic equationsand connected the models to field data. …”
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INVESTIGATION OF HYDRAULIC OPERATIONAL REGIMES OF CIRCULATING SYSTEM AT THERMAL POWER PLANT OF VOLZHSKY AUTOMOTIVE WORKS USING COMPUTER MODEL by V. V. Dikop, A. V. Bukhtiarov, A. G. Kovalenko, V. V. Kotov, V. A. Kudinov

“…The models simulates hydraulic processes by means of an iterated solution of a set of algebraic non-linear equations that is formed while using a graph theory The circulating system is considered as a unit in the model. …”
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On Couple-Group Consensus of Multiagent Networks with Communication and Input Time Delays by Liang-hao Ji, Xin-yue Zhao

“…Based on the frequency-domain theory, some algebraic criteria are addressed analytically. From the results, it is found that the input time delays and the coupling strengths between agents of the systems play a crucial role in reaching group consensus. …”
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Generalized Difference Lacunary Weak Convergence of Sequences by Bibhajyoti Tamuli, Binod Tripathy

“…We investigated several of its algebraic and topological properties, such as solidness, symmetry and monotone. …”
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Spectral Distribution of Transport Operator Arising in Growing Cell Populations by Hongxing Wu, Shenghua Wang, Dengbin Yuan

“…It is to prove that the transport operator AH generates a C0 semigroup and the ninth-order remainder term R9(t) of the Dyson-Phillips expansion of the semigroup is compact, and the spectrum of transport operator AH consists of only finite isolated eigenvalues with finite algebraic multiplicities in a trip Γω. The main methods rely on theory of linear operators, comparison operators, and resolvent operators approach.…”
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On fractional Pennes bio-heat equation using Legendre collocation method by Arvind Kumar Mishra, Sushil Kumar, Ajay Kumar Shukla

“…The best feature of the proposed technique is the conversion of fractional-order differential equations into a set of algebraic systems and the ability to approximate both spatial and temporal coordinates with a single basis. …”
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