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Relevant bibliographies by topics / Algebraic difference equation

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Academic literature on the topic 'Algebraic difference equation'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Algebraic difference equation"

1

Arreche, Carlos E. "Computation of the difference-differential Galois group and differential relations among solutions for a second-order linear difference equation." Communications in Contemporary Mathematics 19, no. 06 (2017): 1650056. http://dx.doi.org/10.1142/s0219199716500565.

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We apply the difference-differential Galois theory developed by Hardouin and Singer to compute the differential-algebraic relations among the solutions to a second-order homogeneous linear difference equation [Formula: see text] where the coefficients [Formula: see text] are rational functions in [Formula: see text] with coefficients in [Formula: see text]. We develop algorithms to compute the difference-differential Galois group associated to such an equation, and show how to deduce the differential-algebraic relations among the solutions from the defining equations of the Galois group.

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Malykh, Mikhail, and Leonid Sevastianov. "Finite Difference Schemes as Algebraic Correspondences between Layers." EPJ Web of Conferences 173 (2018): 03016. http://dx.doi.org/10.1051/epjconf/201817303016.

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For some differential equations, especially for Riccati equation, new finite difference schemes are suggested. These schemes define protective correspondences between the layers. Calculation using these schemes can be extended to the area beyond movable singularities of exact solution without any error accumulation.

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Skovpen, Sergey Mikhailovich, and Albert Saitovich Iskhakov. "Exact Solution of a Linear Difference Equation in a Finite Number of Steps." JOURNAL OF ADVANCES IN MATHEMATICS 14, no. 1 (2018): 7560–63. http://dx.doi.org/10.24297/jam.v14i1.7206.

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An exact solution of a linear difference equation in a finite number of steps has been obtained. This refutes the conventional wisdom that a simple iterative method for solving a system of linear algebraic equations is approximate. The nilpotency of the iteration matrix is the necessary and sufficient condition for getting an exact solution. The examples of iterative equations providing an exact solution to the simplest algebraic system are presented.

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A.S., Iskhakov, and Skovpen S.M. "Exact Solution of a Linear Difference Equation in a Finite Number of Steps." Journal of Progressive Research in Mathematics 13, no. 2 (2018): 2259–62. https://doi.org/10.5281/zenodo.3974630.

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An exact solution of a linear difference equation in a finite number of steps has been obtained. This refutes the conventional wisdom that a simple iterative method for solving a system of linear algebraic equations is approximate. The nilpotency of the iteration matrix is the necessary and sufficient condition for getting an exact solution. The examples of iterative equations providing an exact solution to the simplest algebraic system are presented.

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Wang, Fang, Yuxue Chen, and Yuting Liu. "Finite Difference and Chebyshev Collocation for Time-Fractional and Riesz Space Distributed-Order Advection–Diffusion Equation with Time-Delay." Fractal and Fractional 8, no. 12 (2024): 700. http://dx.doi.org/10.3390/fractalfract8120700.

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In this paper, we have established a numerical method for a class of time-fractional and Riesz space distributed-order advection–diffusion equation with time-delay. Firstly, we transform the Riesz space distributed-order derivative term of the diffusion equation into multi-term fractional derivatives by using the Gauss quadrature formula. Secondly, we discretize time by using second-order finite differences, discretize space by using second kind Chebyshev polynomials, and convert the multi-term fractional equation to a system of algebraic equations. Finally, we solve the algebraic equations by

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Zheng, Xiu-Min, Zong-Xuan Chen, and Tu Jin. "Growth of meromorphic solutions of some difference equations." Applicable Analysis and Discrete Mathematics 4, no. 2 (2010): 309–21. http://dx.doi.org/10.2298/aadm100512022z.

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We investigate higher order difference equations and obtain some results on the growth of transcendental meromorphic solutions, which are complementary to the previous results. Examples are also given to show the sharpness of these results. We also investigate the growth of transcendental entire solutions of a homogeneous algebraic difference equation by using the difference analogue of Wiman-Valiron Theory.

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DOBREV, V. K., H. D. DOEBNER, and C. MRUGALLA. "DIFFERENCE ANALOGUES OF THE FREE SCHRÖDINGER EQUATION." Modern Physics Letters A 14, no. 17 (1999): 1113–22. http://dx.doi.org/10.1142/s021773239900119x.

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We propose an infinite family of difference equations, which are derived from the first principle that they are invariant with respect to the Schrödinger algebra. The first member of this family is a difference analogue of the free Schrödinger equation. These equations are obtained via a purely algebraic construction from a corresponding family of singular vectors in Verma modules over the Schrödinger algebra. The crucial moment in the construction is the realization of the Schrödinger algebra through additive difference vector fields, i.e. vector fields with difference operators instead of di

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Suliman, Tammam, Uta Berger, Marieke Van der Maaten-Theunissen, Ernst Van der Maaten, and Wael Ali. "Modeling dominant height growth using permanent plot data for Pinus brutia stands in the Eastern Mediterranean region." Forest Systems 30, no. 1 (2021): eSC03. http://dx.doi.org/10.5424/fs/2021301-17687.

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Aim of the study: At current, forest management in the Eastern Mediterranean region is largely based on experience rather than on management plans. To support the development of such plans, this study develops and compares site index equations for pure even-aged Pinus brutia stands in Syria using base-age invariant techniques that realistically describe dominant height growth.Materials and methods: Data on top height and stand age were obtained in 2008 and 2016 from 80 permanent plots capturing the whole range of variation in site conditions, stand age and stand density. Both the Algebraic Dif

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Zhang, Xiaojing, Vladimir Gerdt, and Yury Blinkov. "Algebraic Construction of a Strongly Consistent, Permutationally Symmetric and Conservative Difference Scheme for 3D Steady Stokes Flow." Symmetry 11, no. 2 (2019): 269. http://dx.doi.org/10.3390/sym11020269.

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By using symbolic algebraic computation, we construct a strongly-consistent second-order finite difference scheme for steady three-dimensional Stokes flow and a Cartesian solution grid. The scheme has the second order of accuracy and incorporates the pressure Poisson equation. This equation is the integrability condition for the discrete momentum and continuity equations. Our algebraic approach to the construction of difference schemes suggested by the second and the third authors combines the finite volume method, numerical integration, and difference elimination. We make use of the technique

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Altürk, Ahmet. "Application of the Bernstein polynomials for solving Volterra integral equations with convolution kernels." Filomat 30, no. 4 (2016): 1045–52. http://dx.doi.org/10.2298/fil1604045a.

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In this article, we consider the second-type linear Volterra integral equations whose kernels based upon the difference of the arguments. The aim is to convert the integral equation to an algebraic one. This is achieved by approximating functions appearing in the integral equation with the Bernstein polynomials. Since the kernel is of convolution type, the integral is represented as a convolution product. Taylor expansion of kernel along with the properties of convolution are used to represent the integral in terms of the Bernstein polynomials so that a set of algebraic equations is obtained.

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Dissertations / Theses on the topic "Algebraic difference equation"

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Hendriks, Peter Anne. "Algebraic aspects of linear differential and difference equations." [S.l. : [Groningen] : s.n.] ; [University Library Groningen] [Host], 1996. http://irs.ub.rug.nl/ppn/153769580.

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El-Nakla, Jehad A. H. "Finite difference methods for solving mildly nonlinear elliptic partial differential equations." Thesis, Loughborough University, 1987. https://dspace.lboro.ac.uk/2134/10417.

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This thesis is concerned with the solution of large systems of linear algebraic equations in which the matrix of coefficients is sparse. Such systems occur in the numerical solution of elliptic partial differential equations by finite-difference methods. By applying some well-known iterative methods, usually used to solve linear PDE systems, the thesis investigates their applicability to solve a set of four mildly nonlinear test problems. In Chapter 4 we study the basic iterative methods and semiiterative methods for linear systems. In particular, we derive and apply the CS, SOR, SSOR methods

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Boquet, Grant Michael. "Geometric Properties of Over-Determined Systems of Linear Partial Difference Equations." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/26352.

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We relate linear constant coefficient systems of partial difference equations (a discretization of a system of linear partial differential equations) satisfying some collection of scalar polynomial equations to systems defined over the coordinate ring of an algebraic variety. This motivates the extension of behavioral systems theory (a generalization of classical systems theory where inputs and outputs are lumped together) to the setting where the ring of operators is an affine domain and the signal space is restricted to signals which satisfy the same scalar polynomial equations. By recognizi

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Hardy, Benjamin Arik. "A New Method for the Rapid Calculation of Finely-Gridded Reservoir Simulation Pressures." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd1123.pdf.

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Roquefeuil, Alexis. "Confluence of quantum K-theory to quantum cohomology for projective spaces." Thesis, Angers, 2019. http://www.theses.fr/2019ANGE0019/document.

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En géométrie algébrique, les invariants de Gromov—Witten sont des invariants énumératifs qui comptent le nombre de courbes complexes dans une variété projective lisse qui vérifient des conditions d’incidence. En 2001, A. Givental et Y.P. Lee ont défini de nouveaux invariants, dits de Gromov—Witten K-théoriques, en remplaçant les définitions cohomologiques dans la construction des invariants de Gromov—Witten par leurs analogues K-théoriques. Une question essentielle est de comprendre comment sont reliées ces deux théories. En 2013, Iritani- Givental-Milanov-Tonita démontrent que les invariants

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Ahmed, Bacha Rekia Meriem. "Sur un problème inverse en pressage de matériaux biologiques à structure cellulaire." Thesis, Compiègne, 2018. http://www.theses.fr/2018COMP2439.

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Cette thèse, proposée dans le cadre du projet W2P1-DECOL (SAS PIVERT), ﬁnancée par le ministère de l’enseignement supérieur est consacrée à l’étude d’un problème inverse de pressage des matériaux biologiques à structure cellulaire. Le but est d’identiﬁer connaissant les mesures du ﬂux d’huile sortant, le coeﬃcient de consolidation du gâteau de pressage et l’inverse du temps caractéristique de consolidation sur deux niveaux : au niveau de la graine de colza et au niveau du gâteau de pressage. Dans un premier temps, nous présentons un système d’équations paraboliques modélisant le problème de pr

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Nteumagne, Bienvenue Feugang. "Continuous symmetries of difference equations." Thesis, 2011. http://hdl.handle.net/10413/9070.

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We consider the study of symmetry analysis of difference equations. The original work done by Lie about a century ago is known to be one of the best methods of solving differential equations. Lie's theory of difference equations on the contrary, was only first explored about twenty years ago. In 1984, Maeda [42] constructed the similarity methods for difference equations. Some work has been done in the field of symmetries of difference equations for the past years. Given an ordinary or partial differential equation (PDE), one can apply Lie algebra techniques to analyze the problem. It i

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Books on the topic "Algebraic difference equation"

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V, Kondratieva M., ed. Differential and difference dimension polynomials. Kluwer Academic, 1999.

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Kondratieva, M. V. Differential and Difference Dimension Polynomials. Springer Netherlands, 1999.

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Ashyralyev, Allaberen. New Difference Schemes for Partial Differential Equations. Birkhäuser Basel, 2004.

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Samarskii, A. A. Difference Schemes with Operator Factors. Springer Netherlands, 2002.

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Shishkin, G. I. Difference methods for singular perturbation problems. Chapman & Hall/CRC, 2008.

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P, Shishkina Lidia, ed. Difference methods for singular perturbation problems. Chapman & Hall/CRC, 2008.

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Dzhamay, Anton, Ken'ichi Maruno, and Christopher M. Ormerod. Algebraic and analytic aspects of integrable systems and painleve equations: AMS special session on algebraic and analytic aspects of integrable systems and painleve equations : January 18, 2014, Baltimore, MD. American Mathematical Society, 2015.

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author, Tomarelli Franco, ed. Discrete dynamical models. Springer, 2014.

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Ramūnas, Garunkštis, ed. The Lerch zeta-function. Kluwer Academic Publishers, 2002.

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Wolfgang, Kliemann, ed. Dynamical systems and linear algebra. American Mathematical Society, 2014.

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Book chapters on the topic "Algebraic difference equation"

1

Enns, Richard H., and George C. McGuire. "Difference Equation Models." In Computer Algebra Recipes. Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0171-4_9.

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Iwasaki, Masashi, Masato Shinjo, Yusaku Yamamoto, et al. "Integrable Systems Related to Matrix LR Transformations." In Advanced Mathematical Science for Mobility Society. Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-99-9772-5_3.

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AbstractThe discrete Toda (dToda) equation, which is a representative integrable system, is the recursion formula of the well-known quotient-difference algorithm for computing the eigenvalues of tridiagonal matrices. In other words, the dToda equation is related to the LR transformations of tridiagonal matrices. In this chapter, by extending the application of LR transformations from tridiagonal to Hessenberg matrices, we capture the discrete hungry Toda (dhToda) and discrete relativistic Toda (drToda) equations, which are extensions of the dToda equation from the perspective of LR transformat

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Zuevsky, Alexander. "Algebraic Properties of the Semi-direct Product of Kac–Moody and Virasoro Lie Algebras and Associated Bi-Hamiltonian Systems." In Differential and Difference Equations with Applications. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-32857-7_1.

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Glick, Max, and Dylan Rupel. "Introduction to Cluster Algebras." In Symmetries and Integrability of Difference Equations. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56666-5_7.

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Gubbiotti, Giorgio. "Integrability of Difference Equations Through Algebraic Entropy and Generalized Symmetries." In Symmetries and Integrability of Difference Equations. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56666-5_3.

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Cohen, Nir. "Algebraic Reflexivity and Local Linear Dependence: Generic Aspects." In Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations. Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0297-0_12.

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Singer, Michael F. "Algebraic and algorithmic aspects of linear difference equations." In Galois Theories of Linear Difference Equations: An Introduction. American Mathematical Society, 2016. http://dx.doi.org/10.1090/surv/211/01.

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Lefebvre, Vladimir A. "Streams of Consciousness and Difference Equations." In Algebra of Conscience. Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-017-0691-9_35.

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Fox, William P., and Robert E. Burks. "Matrix Algebra Review." In Introduction to Differential and Difference Equations through Modeling. Chapman and Hall/CRC, 2025. https://doi.org/10.1201/9781003582274-1.

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Zuevsky, Alexander. "Geometric Versus Automorphic Correspondence for Vertex Operator Algebra Modules." In Differential and Difference Equations with Applications. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-75647-9_50.

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Conference papers on the topic "Algebraic difference equation"

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Warnecke, Torben, and Gerwald Lichtenberg. "Hybrid implicit multilinear simulation using difference algebraic equations reordering by sparsity patterns^*." In 2024 10th International Conference on Control, Decision and Information Technologies (CoDIT). IEEE, 2024. http://dx.doi.org/10.1109/codit62066.2024.10708218.

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Farouki, Rida T., and Jean-Claude A. Chastang. "Wave-front propagation from exact algebraic equations." In OSA Annual Meeting. Optica Publishing Group, 1990. http://dx.doi.org/10.1364/oam.1990.mgg4.

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Wave fronts in isotropic media can, by Huygens’ principle, be described as envelopes of circles. By using this fact and the appropriate elimination method, the exact algebraic expression for the anticaustics of all the usual optical surfaces in reflection and refraction are derived for a finite distance source. An anticaustic is a wave front of zero optical-path difference. Once the equation of the anticaustic is known, the equation of the parallel wave front corresponding to any optical path difference can be formally found by the same process, although this time the computations are consider

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Kosasih, Engkos Achmad, and Raldi Artono Koestoer. "Determination of Air Temperature Distribution in the Annular Space Using Finite Difference Method." In ASME 1993 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/cie1993-0057.

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Abstract This papers discusses air temperature distribution in the annular space on forced convection of turbulent air flow, which have been determined using numerical method, and compares the result with experimental data. Partial Differential Equations are presented in the final formulation, whereas turbulent flow model applied the simple algebraic model. These equations are changed into numerical equations by means of Finite Difference Method, in the form of explicit equation systems. The steps for solving these systems will be discussed. The comparison between numerical solutions and exper

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Xia, Z. Z., P. Zhang, and R. Z. Wang. "A Novel Finite Difference Method for Flow Calculation on Colocated Grids." In ASME 2008 Heat Transfer Summer Conference collocated with the Fluids Engineering, Energy Sustainability, and 3rd Energy Nanotechnology Conferences. ASMEDC, 2008. http://dx.doi.org/10.1115/ht2008-56265.

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A new finite difference method, which removes the need for staggered grids in fluid dynamic computation, is presented. Pressure checker boarding is prevented through a dual-velocity scheme that incorporates the influence of pressure on velocity gradients. A supplementary velocity resulting from the discrete divergence of pressure gradient, together with the main velocity driven by the discretized pressure first-order gradient, is introduced for the discretization of continuity equation. The method in which linear algebraic equations are solved using incomplete LU factorization, removes the pre

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Campo, Antonio. "Approximate Temperature Profiles and Companion Heat Transfer Rates of Uniform Annular Fins Using Finite-Differences Instead of Bessel Functions." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-1144.

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Abstract The temperature variation along annular fins of uniform thickness and constant thermal conductivity is governed by a differential equation of second order with variable coefficients which is called the modified Bessel equation of zero order. This educational paper addresses a simplistic finite-difference procedure for solving this kind of Bessel equation employing a reduced system of algebraic equations. Approximate temperature distributions and companion heat transfer rates have been computed with the elimination of unknowns by hand and also with the Gauss elimination method using th

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Vanderploeg, Martin J., and Jeff D. Trom. "Automated Linearization of Nonlinear Coupled Differential and Algebraic Equations." In ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0121.

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Abstract This paper presents a new approach for linearization of large multi-body dynamic systems. The approach uses an analytical differentiation of terms evaluated in a numerical equation formulation. This technique is more efficient than finite difference and eliminates the need to determine finite difference pertubation values. Because the method is based on a relative coordinate formalism, linearizations can be obtained for equilibrium configurations with non-zero Cartesian accelerations. Examples illustrate the accuracy and efficiency of the algorithm, and its ability to compute lineariz

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Yaonan, Hua, and Wu Wenquan. "Numerical Solution of Transonic Stream Function Equation on S1 Stream Surface in Cascade." In ASME 1986 International Gas Turbine Conference and Exhibit. American Society of Mechanical Engineers, 1986. http://dx.doi.org/10.1115/86-gt-110.

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A method is presented in this paper for calculating transonic flow field in turbomachinery cascades. With respect to non-orthogoanl curvilinear coordinates, the stream function equation governing fluid flow was established. Using the Artificial Compressibility Method, the discretization of the partial differential equation was carried out by use of the standard central difference formula. The set of linear algebraic equations obtained is solved by means of the Direct Matrix Method. In order to overcome the non-uniqueness of density in transonic flow in the stream function method, the velocitie

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Qingquan, Pan, Lu Haoliang, Li Dongsheng, and Wang Kan. "Study on Semi-Analytical Nodal Method for Solving SP3 Equation." In 2017 25th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/icone25-67597.

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Solving the SP3 equation is the key technology of the Next Generation Reactor Physics Calculation, and has been widely concerned. The semi-analytical nodal method (SANM) based on transverse-integrated neutron diffusion equation has the advantages of high accuracy and convenience for multi-group calculation. The 0th-order flux and the 2nd-order flux being Expanded with the existing 4th-order SANM polynomials and being solved respectively, the 4th-order algebraic accuracy flux distribution is also obtained, however, this solving process is not the semi-analytical nodal method since the polynomia

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Srikanth, D. V. "Oil Film Angular Stiffness Determination in a Hydroelectric Tilting Pad Thrust Bearing." In STLE/ASME 2010 International Joint Tribology Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ijtc2010-41134.

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Tilting pad thrust bearings are designed to transfer high axial loads from rotating shafts to the static support structure. In the present paper, formulation of Reynolds’ equation for the bearing is done in two dimensions (planar). A finite difference method is used to convert the terms of the Reynolds’ equation in to a set of simultaneous linear algebraic equations. A solution procedure for finding value of the pressure in the oil film is described. Numerical integration of the pressure values gives the load distribution. Subsequently, the study of angular stiffness of the film is done by var

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Najjar, Fady M., and Rajat Mittal. "Simulations of Complex Flows and Fluid-Structure Interaction Problems on Fixed Cartesian Grids." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45577.

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A finite-difference based approach for computing flows with complex moving solid three-dimensional boundaries on fixed Cartesian grid has been developed. Internal solid boundaries are represented by “blocking off” the grid cells inside the boundary. This results in considerably increased computing efficiency over conventional body-conformal structured grid methods. A mixed explicit-implicit fractional step method is employed for time integration while the spatial discretization scheme is based on a second-order accurate central-difference scheme. The pressure Poisson equation is solved using a

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