A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain by Faezeh Toutounian, Emran Tohidi, Stanford Shateyi

“…This matrix equation corresponds to a system of linear algebraic equations. By solving this system, the unknown Bernoulli coefficients are determined and thus the approximate solutions are obtained. …”
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Lagrangians, Gauge Functions, and Lie Groups for Semigroup of Second-Order Differential Equations by Z. E. Musielak, N. Davachi, M. Rosario-Franco

“…A set of linear second-order differential equations is converted into a semigroup, whose algebraic structure is used to generate novel equations. …”
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Higher Order Compact Finite Difference Schemes for Unsteady Boundary Layer Flow Problems by P. G. Dlamini, S. S. Motsa, M. Khumalo

“…The CFDRM utilizes the Gauss-Seidel approach of decoupling algebraic equations to linearize the governing equations and solve the resulting system of ordinary differential equations using compact finite difference schemes. …”
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Numerical Solution of Piecewise Constant Delay Systems Based on a Hybrid Framework by H. R. Marzban, S. Hajiabdolrahmani

“…The operational matrices of integration, delay, and product are employed to transform the problem under consideration into a system of algebraic equations. It is shown that the developed approach is also applicable to a special class of nonlinear piecewise constant delay differential equations. …”
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A Global Optimization Algorithm for Signomial Geometric Programming Problem by Xue-Ping Hou, Pei-Ping Shen, Yong-Qiang Chen

“…In the algorithm, by the straight forward algebraic manipulation of terms and by utilizing a transformation of variables, the initial nonconvex programming problem (SGP) is first converted into an equivalent monotonic optimization problem and then is reduced to a sequence of linear programming problems, based on the linearizing technique. …”
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Approximation Technique for Solving Linear Volterra Integro-Differential Equations with Boundary Conditions by Mohamed E. A. Alnair, Ahmed A. Khidir

“…The application of the proposed method leads the Volterra integro-differential equation to a system of algebraic equations that are easy to solve. Some examples are introduced and the obtained results are compared with exact solution as well as the methods that reported in the literature to illustrate the effectiveness and accuracy of the method. …”
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A New Technique for Solving Neutral Delay Differential Equations Based on Euler Wavelets by Mutaz Mohammad, Alexander Trounev

“…Based on the operational matrix, the neutral delay differential equations are reduced to a system of algebraic equations, which is solved through a numerical algorithm. …”
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Bifurcation Analysis of a Singular Bioeconomic Model with Allee Effect and Two Time Delays by Xue Zhang, Qing-ling Zhang, Zhongyi Xiang

“…The singular prey-predator model is transformed into its normal form by using differential-algebraic system theory. We study its dynamics in terms of local analysis and Hopf bifurcation. …”
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A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams by Issam El Hantati, Ahmed Adri, Hatim Fakhreddine, Said Rifai, Rhali Benamar

“…Discrete expressions of the strain energy and kinetic energies are derived, and Hamilton’s principle is applied to reduce the problem to a solution of a nonlinear algebraic system and then solved by an approximate method. …”
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Sphere quantization of Higgs and Coulomb branches and Analytic Symplectic Duality by Davide Gaiotto

“…Localization formulae and dualities applied to these quantizations result in a body of predictions about unitary representations of certain algebras, which may perhaps be understood as an “analytic” form of the symplectic duality program. …”
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Euler Operational Matrix of Integration and Collocation Method for Solving Functional Integral Equations by Sohrab Bazm, Fatemeh Pahlevani

“…This approach transforms the integral equation into a set of nonlinear algebraic equations, which can be efficiently solved by employing standard numerical methods like Newton's method or Picard iteration. …”
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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. …”
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Eigenvalue Based Approach for Global Consensus in Multiagent Systems with Nonlinear Dynamics by Wei Qian, Lei Wang

“…The analytical result shows that, for a weakly connected communication graph, the algebraic connectivity of a redefined symmetric matrix associated with the directed graph is used to evaluate the global consensus of the multiagent system with nonlinear dynamics under the common linear consensus protocol. …”
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Analysis of the growth kinetics of Fe2B layers by the integral method by Keddam M., Kulka M.

“…The set of differential algebraic equations (DAE) system was obtained to estimate the value of activation energy for boron diffusion when pack-boriding of Armco iron in the range of 1123 to 1273 K taking into account the boride incubation time. …”
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Stanley Depth of the Edge Ideal of Extended Gear Networks and Application in Circuit Analysis by Guiling Zeng, Muhammad Mobeen Munir, Raheel Farooki, Muhammad Athar, Jia Bao Liu

“…Stanley depth is a geometric invariant of the module which is closely related to an algebraic invariant called depth of the module. At first, we propose a generalization of classical gear graph and extended m−level gear graph and then establish general closed formulas for the sharp bounds of Stanley depth of quotient of edge ideals associated to extended m-level gear graph. …”
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Bifurcation Analysis and Chaos Control in a Discrete-Time Predator-Prey System of Leslie Type with Simplified Holling Type IV Functional Response by S. M. Sohel Rana, Umme Kulsum

“…The dynamic behavior of a discrete-time predator-prey system of Leslie type with simplified Holling type IV functional response is examined. We algebraically show that the system undergoes a bifurcation (flip or Neimark-Sacker) in the interior of R+2. …”
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Collocation Method Based on Genocchi Operational Matrix for Solving Generalized Fractional Pantograph Equations by Abdulnasir Isah, Chang Phang, Piau Phang

“…Collocation method based on these operational matrices is applied to reduce the generalized fractional pantograph equations to a system of algebraic equations. The comparison of the numerical results with some existing methods shows that the present method is an excellent mathematical tool for finding the numerical solutions of generalized fractional pantograph equations.…”
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Stability Analysis of Fractional-Order Bidirectional Associative Memory Neural Networks with Mixed Time-Varying Delays by Zhanying Yang, Jie Zhang

“…In particular, these obtained conditions are expressed as some algebraic inequalities which can be easily calculated in practical applications. …”
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Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems by Hong Shi, Guangming Xie

“…Our criteria are of the geometric type, and they can be transformed into algebraic type conveniently. Finally, a numerical example is given to illustrate the utility of our criteria.…”
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Alternative Legendre Polynomials Method for Nonlinear Fractional Integro-Differential Equations with Weakly Singular Kernel by Guodong Shi, Yanlei Gong, Mingxu Yi

“…The operational matrices of integration and product together with the derived operational matrix are utilized to transform nonlinear fractional integro-differential equations to the nonlinear system of algebraic equations. Furthermore, the proposed method has also been analyzed for convergence, particularly in context of error analysis. …”
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