Log in

Relevant bibliographies by topics / Differential equations system

Contents

Journal articles
Dissertations / Theses
Books
Book chapters
Conference papers
Reports

Academic literature on the topic 'Differential equations system'

Author: Grafiati

Published: 5 June 2025

Last updated: 24 June 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Differential equations system.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Differential equations system"

1

Esanov, Nuriddin Kurbanovich. "RESOLVING SYSTEM OF DIFFERENTIAL EQUATIONS." Modern Scientific Research International Scientific Journal 2, no. 1 (2024): 241–45. https://doi.org/10.5281/zenodo.10640698.

Full text

Abstract:

This paper mainly used moment equations along the longitudinal, transverse and <em>x</em>, <em>y</em> axes. In this system of six differential equilibrium equations, the force coefficients are calculated as seven. Taking into account the system of equations (1), the system of linear equations was reduced to five equations. After finding the components of deformation from the system of equations (5) - (8), the forces in the state of deformation are found using elasticity relations (1). If we accept , then (5)-(7) are translated into a system of four equations for an open profile rod.

APA, Harvard, Vancouver, ISO, and other styles

2

Alcorta-García, María Aracelia, Martín Eduardo Frías-Armenta, María Esther Grimaldo-Reyna, and Elifalet López-González. "Algebrization of Nonautonomous Differential Equations." Journal of Applied Mathematics 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/632150.

Full text

Abstract:

Given a planar system of nonautonomous ordinary differential equations,dw/dt=F(t,w), conditions are given for the existence of an associative commutative unital algebraAwith uniteand a functionH:Ω⊂R2×R2→R2on an open setΩsuch thatF(t,w)=H(te,w)and the mapsH1(τ)=H(τ,ξ)andH2(ξ)=H(τ,ξ)are Lorch differentiable with respect toAfor all(τ,ξ)∈Ω, whereτandξrepresent variables inA. Under these conditions the solutionsξ(τ)of the differential equationdξ/dτ=H(τ,ξ)overAdefine solutions(x(t),y(t))=ξ(te)of the planar system.

APA, Harvard, Vancouver, ISO, and other styles

3

Petryna, G., and A. Stanzhytskyi. "APPROXIMATION OF STOCHASTIC DELAY DIFFERENTIAL SYSTEMS BY A STOCHASTIC SYSTEM WITHOUT DELAY." Bukovinian Mathematical Journal 12, no. 1 (2024): 120–36. http://dx.doi.org/10.31861/bmj2024.01.11.

Full text

Abstract:

In this paper, we propose a scheme for approximating the solutions of stochastic differential equations with delay by solutions of stochastic differential equations without delay. Stochastic delay differential equations play a crucial role in modeling real-world processes where the evolution depends on past states, introducing complexities due to their infinite-dimensional phase space. To overcome these difficulties, we develop an approach based on approximating the delay system by an ordinary differential equation system of increased dimension. Our main result is to prove that, under certain conditions, the solutions of the approximating system converge in the mean square sense to the solutions of the original delay system. This approach allows for effective analysis and modeling of stochastic systems with delay using finite-dimensional stochastic differential equations without delay.

APA, Harvard, Vancouver, ISO, and other styles

4

BILYI, Leonid, Oleh POLISHCHUK, Svitlana LISEVICH, Anatoly ZALIZETSKY, and Vasiliy MELNIK. "MODELING OF NONLINEAR DYNAMIC SYSTEMS ON THE BASIS OF THE SYSTEM SENSITIVITY MODEL TO ITS INITIAL CONDITIONS." Herald of Khmelnytskyi National University. Technical sciences 309, no. 3 (2022): 99–103. http://dx.doi.org/10.31891/2307-5732-2022-309-3-99-103.

Full text

Abstract:

A typical approach for building and analyzing an object model is presented. It is determined that the tasks of analysis of nonlinear systems consist of: calculation of transients and established processes; determination of static and dynamic stability of the found processes; calculation of the sensitivity of the initial characteristics of the system to changes in its internal and external parameters. It is established that the efficiency of the analysis as a whole is determined not only by the efficiency of the algorithms of each of the stages of calculation, but also by the consistency of the mathematical apparatus that underlies them. It is determined that the calculation of transients is reduced to a problem with initial conditions in which the values of dependent variables are set for the same value of the independent variable, namely time. It is determined that nonlinear dynamic systems whose models are built on the qualitative theory of general differential equations are the main tool for solving many practical problems. It is established that this is explained by the following factors: the presence of a well-developed analytical apparatus and numerous methods of solving general differential equations; transparency and naturalness of general differential equations as a mathematical model to describe the process of transition of real objects from one state to another for external and internal causes; The availability of public qualitative methods of studying decisions of general differential equations, in particular methods of evaluation of stability, analysis of behavior within special points and their asymptotic behavior. The circumstances that lead to the fact that the systems described by conventional differential equations are a methodically very convenient material to create general algorithms for the study of dynamic systems. A mathematical model of sensitivity to the initial conditions is constructed on the basis of heterogeneous differential equations of the first variation, which opens up opportunities for solving the basic problems of analysis, which are: calculation of transitional processes and processes that have been established; Determination of static stability and calculation of parametric sensitivity, on the basis of a single algorithm for solving a two-point T-periodic marginal problem for conventional nonlinear differential equations.

APA, Harvard, Vancouver, ISO, and other styles

5

Cai, Xin. "Numerical Simulation for the System of Ordinary Differential Equations." Advanced Materials Research 179-180 (January 2011): 37–42. http://dx.doi.org/10.4028/www.scientific.net/amr.179-180.37.

Full text

Abstract:

Two coupled small parameter ordinary differential equations were considered. The solutions of differential equations will change rapidly near both sides of the boundary layer. Firstly, the properties were studied for differential equations. Secondly, the asymptotic properties of differential equations were discussed. Thirdly, the numerical methods with zero approximation were constructed for both left side and right side singular component differential equations. Finally, error analyses were given.

APA, Harvard, Vancouver, ISO, and other styles

6

Zhuk, Anastasia I., and Helena N. Zashchuk. "On associated solutions of the system of non-autonomous differential equations in the Lebesgue spaces." Journal of the Belarusian State University. Mathematics and Informatics, no. 1 (April 14, 2022): 6–13. http://dx.doi.org/10.33581/2520-6508-2022-1-6-13.

Full text

Abstract:

Herein, we investigate systems of non-autonomous differential equations with generalised coefficients using the algebra of new generalised functions. We consider a system of non-autonomous differential equations with generalised coefficients as a system of equations in differentials in the algebra of new generalised functions. The solution of such a system is a new generalised function. It is shown that the different interpretations of the solutions of the given systems can be described by a unique approach of the algebra of new generalised functions. In this paper, for the first time in the literature, we describe associated solutions of the system of non-autonomous differential equations with generalised coefficients in the Lebesgue spaces Lp(T).

APA, Harvard, Vancouver, ISO, and other styles

7

Sujito, S., L. Liliasari, and A. Suhandi. "Differential equations: Solving the oscillation system." Journal of Physics: Conference Series 1869, no. 1 (2021): 012163. http://dx.doi.org/10.1088/1742-6596/1869/1/012163.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Brennan, Micheal, and Finbarr Holland. "Linear System of Impulsive Differential Equations." Irish Mathematical Society Bulletin 0038 (1997): 9–20. http://dx.doi.org/10.33232/bims.0038.9.20.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Abirov, A. K., N. K. Shazhdekeeva, and T. N. Akhmurzina. "DIFFERENTIAL EQUATIONS IN A HYPERCOMPLEX SYSTEM." BULLETIN Series of Physics & Mathematical Sciences 69, no. 1 (2020): 7–11. http://dx.doi.org/10.51889/2020-1.1728-7901.01.

Full text

Abstract:

The article considers the problem of solving an inhomogeneous first-order differential equation with a variable with a constant coefficient in a hypercomplex system. The structure of the solution in different cases of the right-hand side of the differential equation is determined. The structure of solving the equation in the case of the appearance of zero divisors is shown. It turns out that when the component of a hypercomplex function is a polynomial of an independent variable, the differential equation turns into an inhomogeneous system of real variables from n equations and its solution is determined by certain methods of the theory of differential equations. Thus, obtaining analytically homogeneous solutions of inhomogeneous differential equations in a hypercomplex system leads to an increase in the efficiency of modeling processes in various fields of science and technology.

APA, Harvard, Vancouver, ISO, and other styles

10

Shan, Li Jun, Xue Fang, and Wei Dong He. "Nonlinear Dynamic Model and Equations of RV Transmission System." Advanced Materials Research 510 (April 2012): 536–40. http://dx.doi.org/10.4028/www.scientific.net/amr.510.536.

Full text

Abstract:

The nonlinear dynamics model of gearing system is developed based on RV transmission system. The influence of the nonlinear factors as time-varying meshing stiffness, backlash of the gear pairs and errors is considered. By means of the Lagrange equation the multi-degree-of-freedom differential equations of motion are derived. The differential equations are very hard to solve for which are characterized by positive semi-definition, time-variation and backlash-type nonlinearity. And linear and nonlinear restoring force are coexist in the equations. In order to solve easily, the differential equations are transformed to identical dimensionless nonlinear differential equations in matrix form. The establishment of the nonlinear differential equations laid a foundation for The Solution of differential equations and the analysis of the nonlinearity characteristics.

APA, Harvard, Vancouver, ISO, and other styles

More sources

Dissertations / Theses on the topic "Differential equations system"

1

Müller, Thorsten G. "Modeling complex systems with differential equations." [S.l. : s.n.], 2002. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10236319.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Gauthier, Genevieve Carleton University Dissertation Mathematics and Statistics. "Multilevel bilinear system of stochastic differential equations." Ottawa, 1995.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

3

Kadamani, Sami M. "USFKAD: An Expert System For Partial Differential Equations." [Tampa, Fla.] : University of South Florida, 2005. http://purl.fcla.edu/fcla/etd/SFE0001144.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Weickert, J. "Navier-Stokes equations as a differential-algebraic system." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800942.

Full text

Abstract:

Nonsteady Navier-Stokes equations represent a differential-algebraic system of strangeness index one after any spatial discretization. Since such systems are hard to treat in their original form, most approaches use some kind of index reduction. Processing this index reduction it is important to take care of the manifolds contained in the differential-algebraic equation (DAE). We investigate for several discretization schemes for the Navier-Stokes equations how the consideration of the manifolds is taken into account and propose a variant of solving these equations along the lines of the theoretically best index reduction. Applying this technique, the error of the time discretisation depends only on the method applied for solving the DAE.

APA, Harvard, Vancouver, ISO, and other styles

5

Chow, Tanya L. M., of Western Sydney Macarthur University, and Faculty of Business and Technology. "Systems of partial differential equations and group methods." THESIS_FBT_XXX_Chow_T.xml, 1996. http://handle.uws.edu.au:8081/1959.7/43.

Full text

Abstract:

This thesis is concerned with the derivation of similarity solutions for one-dimensional coupled systems of reaction - diffusion equations, a semi-linear system and a one-dimensional tripled system. The first area of research in this thesis involves a coupled system of diffusion equations for the existence of two distinct families of diffusion paths. Constructing one-parameter transformation groups preserving the invariance of this system of equations enables similarity solutions for this coupled system to be derived via the classical and non-classical procedures. This system of equation is the uncoupled in the hope of recovering further similarity solutions for the system. Once again, one-parameter groups leaving the uncoupled system invariant are obtained, enabling similarity solutions for the system to be elicited. A one-dimensional pattern formation in a model of burning forms the next component of this thesis. The primary focus of this area is the determination of similarity solutions for this reaction - diffusion system by means of one-parameter transformation group methods. Consequently, similarity solutions which are a generalisation of the solutions of the one-dimensional steady equations derived by Forbes are deduced. Attention in this thesis is then directed toward a semi-linear coupled system representing a predator - prey relationship. Two approaches to solving this system are made using the classical procedure, leading to one-parameter transformation groups which are instrumental in elicting the general similarity solution for this system. A triple system of equations representing a one-dimensional case of diffusion in the presence of three diffusion paths constitutes the next theme of this thesis. In association with the classical and non-classical procedures, the derivation of one-parameter transformation groups leaving this system invariant enables similarity solutions for this system to be deduced. The final strand of this thesis involves a one- dimensional case of the general linear system of coupled diffusion equations with cross-effects for which one-parameter transformation group methods are once more employed. The one-parameter groups constructed for this system prove instrumental in enabling the attainment of similarity solutions for this system to be accomplished<br>Faculty of Business and Technology

APA, Harvard, Vancouver, ISO, and other styles

6

Lee, Hwasung. "Strominger's system on non-Kähler hermitian manifolds." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:d3956c4f-c262-4bbf-8451-8dac35f6abef.

Full text

Abstract:

In this thesis, we investigate the Strominger system on non-Kähler manifolds. We will present a natural generalization of the Strominger system for non-Kähler hermitian manifolds M with c₁(M) = 0. These manifolds are more general than balanced hermitian manifolds with holomorphically trivial canonical bundles. We will then consider explicit examples when M can be realized as a principal torus fibration over a Kähler surface S. We will solve the Strominger system on such construction which also includes manifolds of topology (k−1)(S²×S⁴)#k(S³×S³). We will investigate the anomaly cancellation condition on the principal torus fibration M. The anomaly cancellation condition reduces to a complex Monge-Ampère-type PDE, and we will prove existence of solution following Yau’s proof of the Calabi-conjecture [Yau78], and Fu and Yau’s analysis [FY08]. Finally, we will discuss the physical aspects of our work. We will discuss the Strominger system using α'-expansion and present a solution up to (α')¹-order. In the α'-expansion approach on a principal torus fibration, we will show that solving the anomaly cancellation condition in topology is necessary and sufficient to solving it analytically. We will discuss the potential problems with α'-expansion approach and consider the full Strominger system with the Hull connection. We will show that the α'-expansion does not correctly capture the behaviour of the solution even up to (α')¹-order and should be used with caution.

APA, Harvard, Vancouver, ISO, and other styles

7

Chow, Tanya L. M. "Systems of partial differential equations and group methods." Thesis, [Campbelltown, N.S.W. : The Author], 1996. http://handle.uws.edu.au:8081/1959.7/43.

Full text

Abstract:

This thesis is concerned with the derivation of similarity solutions for one-dimensional coupled systems of reaction - diffusion equations, a semi-linear system and a one-dimensional tripled system. The first area of research in this thesis involves a coupled system of diffusion equations for the existence of two distinct families of diffusion paths. Constructing one-parameter transformation groups preserving the invariance of this system of equations enables similarity solutions for this coupled system to be derived via the classical and non-classical procedures. This system of equation is the uncoupled in the hope of recovering further similarity solutions for the system. Once again, one-parameter groups leaving the uncoupled system invariant are obtained, enabling similarity solutions for the system to be elicited. A one-dimensional pattern formation in a model of burning forms the next component of this thesis. The primary focus of this area is the determination of similarity solutions for this reaction - diffusion system by means of one-parameter transformation group methods. Consequently, similarity solutions which are a generalisation of the solutions of the one-dimensional steady equations derived by Forbes are deduced. Attention in this thesis is then directed toward a semi-linear coupled system representing a predator - prey relationship. Two approaches to solving this system are made using the classical procedure, leading to one-parameter transformation groups which are instrumental in elicting the general similarity solution for this system. A triple system of equations representing a one-dimensional case of diffusion in the presence of three diffusion paths constitutes the next theme of this thesis. In association with the classical and non-classical procedures, the derivation of one-parameter transformation groups leaving this system invariant enables similarity solutions for this system to be deduced. The final strand of this thesis involves a one- dimensional case of the general linear system of coupled diffusion equations with cross-effects for which one-parameter transformation group methods are once more employed. The one-parameter groups constructed for this system prove instrumental in enabling the attainment of similarity solutions for this system to be accomplished

APA, Harvard, Vancouver, ISO, and other styles

8

Baugh, James Emory. "Group analysis of a system of reaction-diffusion equations." Thesis, Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/28554.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Foley, Dawn Christine. "Applications of State space realization of nonlinear input/output difference equations." Thesis, Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/16818.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Ahlip, Rehez Ajmal. "Stability & filtering of stochastic systems." Thesis, Queensland University of Technology, 1997.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

More sources

Books on the topic "Differential equations system"

1

Ilchmann, Achim. Surveys in Differential-Algebraic Equations I. Springer Berlin Heidelberg, 2013.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

2

Maury, Bertrand. The Respiratory System in Equations. Springer Milan, 2013.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

3

Arendt, Wolfgang, Joseph A. Ball, Jussi Behrndt, Karl-Heinz Förster, Volker Mehrmann, and Carsten Trunk, eds. 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.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Verhulst, Ferdinand. Nonlinear differential equations and dynamical systems. Springer-Verlag, 1990.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

5

Arrowsmith, D. K. Dynamical systems: Differential equations, maps, and chaotic behaviour. Chapman & Hall, 1992.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

6

Arrowsmith, D. K. Dynamical systems: Differential equations, maps, and chaotic behaviour. Chapman & Hall, 1998.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

7

Arrowsmith, D. K. Dynamical systems: Differential equations, maps and chaotic behaviour. Chapman & Hall, 1992.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

8

Kunita, Hiroshi. Stochastic flows and stochastic differential equations. Cambridge UniversityPress, 1990.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

9

Vidyasagar, M. Non-linear systems analysis. 2nd ed. Prentice-Hall International (UK), 1993.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

10

Kaikko, Juha. Performance prediction of gas turbines by solving a system of non-linear equations. Lappeenranta University of Technology, 1998.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

More sources

Book chapters on the topic "Differential equations system"

1

Gad, Osama. "System Differential Equations Solution." In System Dynamics. CRC Press, 2024. http://dx.doi.org/10.1201/9781032685656-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Devi, J. Vasundhara, Sadashiv G. Deo, and Ramakrishna Khandeparkar. "Linear System of Equations." In Linear Algebra to Differential Equations. Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781351014953-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Shima, Hiroyuki, and Tsuneyoshi Nakayama. "System of Ordinary Differential Equations." In Higher Mathematics for Physics and Engineering. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/b138494_16.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Gupta, Abhishek K. "Differential Equations and System Dynamics." In Numerical Methods using MATLAB. Apress, 2014. http://dx.doi.org/10.1007/978-1-4842-0154-1_10.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Kolk, W. Richard, and Robert A. Lerman. "Analytic Solutions to Nonlinear Differential Equations." In Nonlinear System Dynamics. Springer US, 1992. http://dx.doi.org/10.1007/978-1-4684-6494-8_3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Ben Amma, Bouchra, Said Melliani, and L. S. Chadli. "Intuitionistic Fuzzy Functional Differential Equations." In Fuzzy Logic in Intelligent System Design. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-67137-6_39.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Horgmo Jæger, Karoline, and Aslak Tveito. "A System of Ordinary Differential Equations." In Differential Equations for Studies in Computational Electrophysiology. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-30852-9_2.

Full text

Abstract:

AbstractWe will introduce numerical methods for systems of ODEs by considering the celebrated FitzHugh-Nagumo model published by FitzHugh [1] in 1961 and, independently, by Nagumo et. al. [2] in 1962. The model is a system of ordinary differential equations with two unknowns, and is commonly used as a simple model for the action potentials of excitable pacemaker cells.

APA, Harvard, Vancouver, ISO, and other styles

8

Meher, Ramakanta. "System of First-Order Differential Equations." In Textbook on Ordinary Differential Equations. River Publishers, 2022. http://dx.doi.org/10.1201/9781003360643-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Ferrareso Lona, Liliane Maria. "Solving an Ordinary Differential Equations System." In A Step by Step Approach to the Modeling of Chemical Engineering Processes. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-66047-9_6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Ferrareso Lona, Liliane Maria. "Solving a Partial Differential Equations System." In A Step by Step Approach to the Modeling of Chemical Engineering Processes. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-66047-9_7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Differential equations system"

1

Zhang, Shaorong, Koji Yamashita, and Nanpeng Yu. "Learning Power System Dynamics with Noisy Data Using Neural Ordinary Differential Equations." In 2024 IEEE Power & Energy Society General Meeting (PESGM). IEEE, 2024. http://dx.doi.org/10.1109/pesgm51994.2024.10689132.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Mahmoud, Ahmed G., Mohamed A. El-Beltagy, and Ahmed M. Zobaa. "Modeling of Commercial Photovoltaic Modules using Fractional Order and Stochastic Differential Equations." In 2024 25th International Middle East Power System Conference (MEPCON). IEEE, 2024. https://doi.org/10.1109/mepcon63025.2024.10850280.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

GAIKO, V. A., and W. T. VAN HORSSEN. "GLOBAL ANALYSIS OF A CANONICAL CUBIC SYSTEM." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0183.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

GELFREICH, V., and L. M. LERMAN. "SLOW MANIFOLDS IN A SINGULARLY PERTURBED HAMILTONIAN SYSTEM." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0146.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

SHCHETININA, E. V. "LOSS OF STABILITY SCENARIO IN THE ZIEGLER SYSTEM." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0153.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

GUZMÁN-GÓMEZ, M. "ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE ZAKHAROV SYSTEM." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0185.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

CASTELLÀ, ENRIC, and ÀNGEL JORBA. "THE LAGRANGIAN POINTS OF THE REAL EARTH-MOON SYSTEM." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0001.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Liu, Yang, and Kai Sun. "Solving Power System Differential Algebraic Equations Using Differential Transformation." In 2020 IEEE Power & Energy Society General Meeting (PESGM). IEEE, 2020. http://dx.doi.org/10.1109/pesgm41954.2020.9281519.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

PETZELTOVÁ, H. "CONVERGENCE OF SOLUTIONS OF A NON-LOCAL PHASE-FIELD SYSTEM WITH MEMORY." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0110.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

GALKIN, V. A. "SINGULARITIES OF THE SOLUTION OF THE INFINITE-DIMENSIONAL HYPERBOLIC SMOLUCHOWSKI SYSTEM DESCRIBING COAGULATION PROCESS." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0082.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Reports on the topic "Differential equations system"

1

Caraus, Lurie, and Zhilin Li. A Direct Method and Convergence Analysis for Some System of Singular Integro-Differential Equations. Defense Technical Information Center, 2003. http://dx.doi.org/10.21236/ada451436.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Landwehr, Philipp, Paulius Cebatarauskas, Csaba Rosztoczy, Santeri Röpelinen, and Maddalena Zanrosso. Inverse Methods In Freeform Optics. Technische Universität Dresden, 2023. http://dx.doi.org/10.25368/2023.148.

Full text

Abstract:

Traditional methods in optical design like ray tracing suffer from slow convergence and are not constructive, i.e., each minimal perturbation of input parameters might lead to “chaotic” changes in the output. However, so-called inverse methods can be helpful in designing optical systems of reflectors and lenses. The equations in R2 become ordinary differential equations, while in R3 the equations become partial differential equations. These equations are then used to transform source distributions into target distributions, where the distributions are arbitrary, though assumed to be positive and integrable. In this project, we derive the governing equations and solve them numerically, for the systems presented by our instructor Martijn Anthonissen [Anthonissen et al. 2021]. Additionally, we show how point sources can be derived as a special case of a interval source with di- rected source interval, i.e., with each point in the source interval there is also an associated unit direction vector which could be derived from a system of two interval sources in R2. This way, it is shown that connecting source distributions with target distributions can be classified into two instead of three categories. The resulting description of point sources as a source along an interval with directed rays could potentially be extended to three dimensions, leading to interpretations of point sources as directed sources on convex or star-shaped sets.

APA, Harvard, Vancouver, ISO, and other styles

3

Shen, Shiyu, Yuhui Zhai, and Yanfeng Ouyang. Planning and Dynamic Management of Autonomous Modular Mobility Services. Illinois Center for Transportation, 2024. https://doi.org/10.36501/0197-9191/24-029.

Full text

Abstract:

As we enter the next era of autonomous driving, robo-vehicles (which serve as low-cost and fully compliant drivers) are replacing conventional chauffeured services in the mobility market. During just the last few years, companies like Waymo Inc. and Cruise Inc. have already offered fully driverless robo-taxi services to the general public in cities like Phoenix and San Francisco. The rapid evolution of autonomous vehicles is anticipated to reshape the shared mobility market very soon. This project aims to address the following open questions. At the operational level, how should modular units be allocated across multiple categories of customers (e.g., passenger and freight cabins), and how should they be matched in real time? How do we enhance system efficiency by dynamic relocation and swap of modular chassis? At the strategic or tactical level, how should the rolling stock resources (modular chassis, passenger and freight cabins) be planned, and where shall chassis swapping sites be located? How could any potential transaction cost for a chassis swap, such as the time required for a modular chassis to be assembled with a customized cabin, affect the optimal strategy and system performance? How can customer priorities (e.g., passenger vs. freight) affect system performance, and how can service providers manage demand by specific pricing scheme or discriminative customer service strategies? We conducted the following research tasks: (i) analytically derived systems of implicit nonlinear equations in the closed form, including a set of differential equations, to analyze the modular autonomous mobility system and to estimate the expected system performance in the steady state; (ii) conducted a series of agent-based simulation experiments to verify the accuracy of the proposed analytical formulas and to demonstrate the effectiveness of the proposed modular chassis services; and (iii) designed policy instruments to enhance transportation system performance.

APA, Harvard, Vancouver, ISO, and other styles

4

Trahan, Corey, Jing-Ru Cheng, and Amanda Hines. ERDC-PT : a multidimensional particle tracking model. Engineer Research and Development Center (U.S.), 2023. http://dx.doi.org/10.21079/11681/48057.

Full text

Abstract:

This report describes the technical engine details of the particle- and species-tracking software ERDC-PT. The development of ERDC-PT leveraged a legacy ERDC tracking model, “PT123,” developed by a civil works basic research project titled “Efficient Resolution of Complex Transport Phenomena Using Eulerian-Lagrangian Techniques” and in part by the System-Wide Water Resources Program. Given hydrodynamic velocities, ERDC-PT can track thousands of massless particles on 2D and 3D unstructured or converted structured meshes through distributed processing. At the time of this report, ERDC-PT supports triangular elements in 2D and tetrahedral elements in 3D. First-, second-, and fourth-order Runge-Kutta time integration methods are included in ERDC-PT to solve the ordinary differential equations describing the motion of particles. An element-by-element tracking algorithm is used for efficient particle tracking over the mesh. ERDC-PT tracks particles along the closed and free surface boundaries by velocity projection and stops tracking when a particle encounters the open boundary. In addition to passive particles, ERDC-PT can transport behavioral species, such as oyster larvae. This report is the first report of the series describing the technical details of the tracking engine. It details the governing equation and numerical approaching associated with ERDC-PT Version 1.0 contents.

APA, Harvard, Vancouver, ISO, and other styles

5

Pasupuleti, Murali Krishna. Mathematical Modeling for Machine Learning: Theory, Simulation, and Scientific Computing. National Education Services, 2025. https://doi.org/10.62311/nesx/rriv125.

Full text

Abstract:

Abstract Mathematical modeling serves as a fundamental framework for advancing machine learning (ML) and artificial intelligence (AI) by integrating theoretical, computational, and simulation-based approaches. This research explores how numerical optimization, differential equations, variational inference, and scientific computing contribute to the development of scalable, interpretable, and efficient AI systems. Key topics include convex and non-convex optimization, physics-informed machine learning (PIML), partial differential equation (PDE)-constrained AI, and Bayesian modeling for uncertainty quantification. By leveraging finite element methods (FEM), computational fluid dynamics (CFD), and reinforcement learning (RL), this study demonstrates how mathematical modeling enhances AI-driven scientific discovery, engineering simulations, climate modeling, and drug discovery. The findings highlight the importance of high-performance computing (HPC), parallelized ML training, and hybrid AI approaches that integrate data-driven and model-based learning for solving complex real-world problems. Keywords Mathematical modeling, machine learning, scientific computing, numerical optimization, differential equations, PDE-constrained AI, variational inference, Bayesian modeling, convex optimization, non-convex optimization, reinforcement learning, high-performance computing, hybrid AI, physics-informed machine learning, finite element methods, computational fluid dynamics, uncertainty quantification, simulation-based AI, interpretable AI, scalable AI.

APA, Harvard, Vancouver, ISO, and other styles

6

Shearer, Michael. Systems of Hyperbolic Partial Differential Equations. Defense Technical Information Center, 1994. http://dx.doi.org/10.21236/ada290287.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Seidman, Thomas I. Nonlinear Systems of Partial Differential Equations. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada217581.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Hale, Jack, Constantine M. Dafermos, John Mallet-Paret, Panagiotis E. Souganidis, and Walter Strauss. Dynamical Systems and Nonlinear Partial Differential Equations. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada255356.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Dafermos, Constantine M., John Mallet-Paret, Panagiotis E. Souganidis, and Walter Strauss. Dynamical Systems and Nonlinear Partial Differential Equations. Defense Technical Information Center, 1993. http://dx.doi.org/10.21236/ada271514.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Shearer, Michael. Systems of Nonlinear Hyperbolic Partial Differential Equations. Defense Technical Information Center, 1997. http://dx.doi.org/10.21236/ada344449.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!