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Academic literature on the topic 'Hybrid differential equations'

Author: Grafiati

Published: 4 June 2025

Last updated: 23 June 2025

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Journal articles on the topic "Hybrid differential equations"

1

Sadhasivam, V., and M. Deepa. "Oscillation criteria for fractional impulsive hybrid partial differential equations." Issues of Analysis 26, no. 2 (2019): 73–91. http://dx.doi.org/10.15393/j3.art.2019.5910.

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Dhage, Bapurao C. "Differential inequalities for hybrid fractional differential equations." Journal of Mathematical Inequalities, no. 3 (2013): 453–59. http://dx.doi.org/10.7153/jmi-07-40.

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Harir, A., S. Melliani, and L. S. Chadli. "Fuzzy fractional hybrid differential equations." Carpathian Mathematical Publications 14, no. 2 (2022): 332–44. http://dx.doi.org/10.15330/cmp.14.2.332-344.

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This article is related to present and solve the theory of fractional hybrid differential equations with fuzzy initial values involving the fuzzy Riemann-Liouville fractional differential operators of order $0 < q < 1$. For the concerned presentation, we study the existence and uniqueness of a fuzzy solution are brought in detail basing on the concept of generalized division of fuzzy numbers. We have developed and investigated a fuzzy solution of a fuzzy fractional hybrid differential equation. At the end we have given an example is provided to illustrate the theory.

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Hilal, Khalid, and Ahmed Kajouni. "Existence of the Solution for System of Coupled Hybrid Differential Equations with Fractional Order and Nonlocal Conditions." International Journal of Differential Equations 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/4726526.

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This paper is motivated by some papers treating the fractional hybrid differential equations with nonlocal conditions and the system of coupled hybrid fractional differential equations; an existence theorem for fractional hybrid differential equations involving Caputo differential operators of order1<α≤2is proved under mixed Lipschitz and Carathéodory conditions. The existence and uniqueness result is elaborated for the system of coupled hybrid fractional differential equations.

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Khan, Subuhi, Mumtaz Riyasat, and Shahid Ahmad Wani. "On some classes of differential equations and associated integral equations for the Laguerre–Appell polynomials." Advances in Pure and Applied Mathematics 9, no. 3 (2018): 185–94. http://dx.doi.org/10.1515/apam-2017-0079.

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Abstract The article aims to explore some new classes of differential equations and associated integral equations for some hybrid families of Laguerre polynomials. The recurrence relations and differential, integro-differential and partial differential equations for the hybrid Laguerre–Appell polynomials are derived via the factorization method. An analogous study of these results for the hybrid Laguerre–Bernoulli, Euler and Genocchi polynomials is presented. Further, the Volterra integral equations for the hybrid Laguerre–Appell polynomials and for their corresponding members are also explored.

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Benallou, Mohamed, Hamid Beddani, and Moustafa Beddani. "Existence of solution for a tripled system of fractional hybrid differential equations with laplacie involving Caputo derivatives." STUDIES IN ENGINEERING AND EXACT SCIENCES 5, no. 2 (2024): e11971. https://doi.org/10.54021/seesv5n2-734.

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In this paper, we study the existence of solutions for a tripled system of Fractional hybrid differential equations with nonlocal integro multi point boundary conditions by using the Laplacian operator of degree p and the Caputo derivatives, we know that the differential equations with the Laplacian operator appeared for the first time when Leibenson was attempting to derive an accurate formula to model turbulent flow in the porous medium, in this work we study the case of the Fractional hybrid differential equations who are the quadratic perturbations of nonlinear differential equations. Dhage and Lakshmikantham [12] discussed the hybrid differential equation They established the existence, uniqueness results, and some fundamental differential inequalities for hybrid differential equations initiating the study of the theory of such systems and proved to utilize the theory of inequalities, its existence of extremal solutions, and comparison results. Hilal and Kajouni [19] have studied boundary fractional hybrid differential equations involving Caputo differential operators, so In this article, we are interested in the existence result of the solution of hybrid nonlinear differential equations. obtained by the hybrid fixed point theorem for a sum of three operators due to Dhage. An illustrative example is presented at the end to show the applicability of the results. To the best of our knowledge, this is the first time where such problem is considered.

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Ivaz, K., A. Khastan, and Juan J. Nieto. "A Numerical Method for Fuzzy Differential Equations and Hybrid Fuzzy Differential Equations." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/735128.

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Numerical algorithms for solving first-order fuzzy differential equations and hybrid fuzzy differential equations have been investigated. Sufficient conditions for stability and convergence of the proposed algorithms are given, and their applicability is illustrated with some examples.

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Herzallah, Mohamed A. E., and Dumitru Baleanu. "On Fractional Order Hybrid Differential Equations." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/389386.

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We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order0<α<1. Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.

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Dhage, Bapurao C., and V. Lakshmikantham. "Basic results on hybrid differential equations." Nonlinear Analysis: Hybrid Systems 4, no. 3 (2010): 414–24. http://dx.doi.org/10.1016/j.nahs.2009.10.005.

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Zhao, Yige, Shurong Sun, Zhenlai Han, and Qiuping Li. "Theory of fractional hybrid differential equations." Computers & Mathematics with Applications 62, no. 3 (2011): 1312–24. http://dx.doi.org/10.1016/j.camwa.2011.03.041.

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Dissertations / Theses on the topic "Hybrid differential equations"

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Wright, S. J. "The application of transmission-line modelling implicit and hybrid algorithms to electromagnetic problems." Thesis, University of Nottingham, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384746.

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Lenz, Simon Manfred [Verfasser], and Hans Georg [Akademischer Betreuer] Bock. "Impulsive Hybrid Discrete-Continuous Delay Differential Equations / Simon Manfred Lenz ; Betreuer: Hans Georg Bock." Heidelberg : Universitätsbibliothek Heidelberg, 2014. http://d-nb.info/1179925408/34.

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Lenz, Simon M. [Verfasser], and Hans Georg [Akademischer Betreuer] Bock. "Impulsive Hybrid Discrete-Continuous Delay Differential Equations / Simon Manfred Lenz ; Betreuer: Hans Georg Bock." Heidelberg : Universitätsbibliothek Heidelberg, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:16-heidok-171173.

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Pierson, Mark A. "Theory and Application of a Class of Abstract Differential-Algebraic Equations." Diss., Virginia Tech, 2005. http://hdl.handle.net/10919/27416.

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We first provide a detailed background of a geometric projection methodology developed by Professor Roswitha Marz at Humboldt University in Berlin for showing uniqueness and existence of solutions for ordinary differential-algebraic equations (DAEs). Because of the geometric and operator-theoretic aspects of this particular method, it can be extended to the case of infinite-dimensional abstract DAEs. For example, partial differential equations (PDEs) are often formulated as abstract Cauchy or evolution problems which we label abstract ordinary differential equations or AODE. Using this abstract formulation, existence and uniqueness of the Cauchy problem has been studied. Similarly, we look at an AODE system with operator constraint equations to formulate an abstract differential-algebraic equation or ADAE problem. Existence and uniqueness of solutions is shown under certain conditions on the operators for both index-1 and index-2 abstract DAEs. These existence and uniqueness results are then applied to some index-1 DAEs in the area of thermodynamic modeling of a chemical vapor deposition reactor and to a structural dynamics problem. The application for the structural dynamics problem, in particular, provides a detailed construction of the model and development of the DAE framework. Existence and uniqueness are primarily demonstrated using a semigroup approach. Finally, an exploration of some issues which arise from discretizing the abstract DAE are discussed.<br>Ph. D.

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Eggers, Andreas [Verfasser], Martin [Akademischer Betreuer] Fränzle, and Nacim [Akademischer Betreuer] Ramdani. "Direct handling of ordinary differential equations in constraint-solving-based analysis of hybrid systems / Andreas Eggers. Betreuer: Martin Fränzle ; Nacim Ramdani." Oldenburg : BIS der Universität Oldenburg, 2014. http://d-nb.info/1056999748/34.

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Marx, Swann. "Méthodes de stabilisation de systèmes non-linéaires avec des mesures partielles et des entrées contraintes." Thesis, Université Grenoble Alpes (ComUE), 2017. http://www.theses.fr/2017GREAT040/document.

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Cette thèse a pour sujet la stabilisation de systèmes non-linéaires avec des mesures partielles et des entrées contraintes. Les deux premiers chapitres traitent du problème des entrées saturées dans le contexte des systèmes de dimension infinie pour des équations nonlinéaires abstraites et une équation aux dérivées partielles nonlinéaire particulière, l'équation de Korteweg-de Vries. Les outils mathématiques utilisés pour obtenir des résultats Le troisième chapitre propose une méthode de synthèse de retour de sortie pour deux équations de Korteweg-de Vries. Le quatrième chapitre concerne la synthèse d'un retour de sortie pour des systèmes non-linéaires de dimension finie pour lequel il existe un contrôle hybride. Une stratégie basée sur des observateurs grand gain est utilisée<br>This thesis is about the stabilization of nonlinear systems with partial measurements and constrained input. The two first chapters deals with saturated inputs in the contex of infinite-dimensional systems for nonlinear abstract equations and for a particular partial differential equation, the Korteweg-de Vries equation. The third chapter provides an output feedback design for two Korteweg-de Vries equations using the backstepping method. The fourth chapter is about the output feedback design of nonlinear finite-dimensional systems for which there exists a hybrid controller. A high-gain observer strategy is used

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Strohm, Christian. "Circuit Simulation Including Full-Wave Maxwell's Equations." Doctoral thesis, Humboldt-Universität zu Berlin, 2021. http://dx.doi.org/10.18452/22544.

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Diese Arbeit widmet sich der Simulation von elektrischen/elektronischen Schaltungen welche um elektromagnetische Bauelemente erweitert werden. Im Fokus stehen unterschiedliche Kopplungen der Schaltungsgleichungen, modelliert mit der modifizierten Knotenanalyse, und den elektromagnetischen Bauelementen mit deren verfeinerten Modell basierend auf den vollen Maxwell-Gleichungen in der Lorenz-geeichten A-V Formulierung welche durch Finite-Integrations-Technik räumlich diskretisiert werden. Eine numerische Analyse erweitert die topologischen Kriterien für den Index der resultierenden differential-algebraischen Gleichungen, wie sie bereits in anderen Arbeiten mit ähnlichen Feld/Schaltkreis-Kopplungen hergeleitet wurden. Für die Simulation werden sowohl ein monolithischer Ansatz als auch Waveform-Relaxationsmethoden untersucht. Im Mittelpunkt stehen dabei Zeitintegration, Skalierungsmethoden, strukturelle Eigenschaften und ein hybride Ansatz zur Lösung der zugrundeliegenden linearen Gleichungssysteme welcher den Einsatz spezialisierter Löser für die jeweiligen Teilsysteme erlaubt. Da die vollen Maxwell-Gleichungen zusätzliche Ableitungen in der Kopplungsstruktur verursachen, sind bisher existierende Konvergenzaussagen für die Waveform-Relaxation von gekoppelten differential-algebraischen Gleichungen nicht anwendbar und motivieren eine neue Konvergenzanalyse. Auf dieser Analyse aufbauend werden hinreichende topologische Kriterien entwickelt, welche eine Konvergenz von Gauß-Seidel- und Jacobi-artigen Waveform-Relaxationen für die gekoppelten Systeme garantieren. Schließlich werden numerische Benchmarks zur Verfügung gestellt, um die eingeführten Methoden und Theoreme dieser Abhandlung zu unterstützen.<br>This work is devoted to the simulation of electrical/electronic circuits incorporating electromagnetic devices. The focus is on different couplings of the circuit equations, modeled with the modified nodal analysis, and the electromagnetic devices with their refined model based on full-wave Maxwell's equations in Lorenz gauged A-V formulation which are spatially discretized by the finite integration technique. A numerical analysis extends the topological criteria for the index of the resulting differential-algebraic equations, as already derived in other works with similar field/circuit couplings. For the simulation, both a monolithic approach and waveform relaxation methods are investigated. The focus is on time integration, scaling methods, structural properties and a hybrid approach to solve the underlying linear systems of equations with the use of specialized solvers for the respective subsystems. Since the full-Maxwell approach causes additional derivatives in the coupling structure, previously existing convergence statements for the waveform relaxation of coupled differential-algebraic equations are not applicable and motivate a new convergence analysis. Based on this analysis, sufficient topological criteria are developed which guarantee convergence of Gauss-Seidel and Jacobi type waveform relaxation schemes for introduced coupled systems. Finally, numerical benchmarks are provided to support the introduced methods and theorems of this treatise.

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Alberti, Giovanni S. "On local constraints and regularity of PDE in electromagnetics : applications to hybrid imaging inverse problems." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:1b30b3b7-29b1-410d-ae30-bd0a87c9720b.

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The first contribution of this thesis is a new regularity theorem for time harmonic Maxwell's equations with less than Lipschitz complex anisotropic coefficients. By using the L<sup>p</sup> theory for elliptic equations, it is possible to prove H<sup>1</sup> and Hölder regularity results, provided that the coefficients are W<sup>1,p</sup> for some p = 3. This improves previous regularity results, where the assumption W<sup>1,∞</sup> for the coefficients was believed to be optimal. The method can be easily extended to the case of bi-anisotropic materials, for which a separate approach turns out to be unnecessary. The second focus of this work is the boundary control of the Helmholtz and Maxwell equations to enforce local constraints inside the domain. More precisely, we look for suitable boundary conditions such that the corresponding solutions and their derivatives satisfy certain local non-zero constraints. Complex geometric optics solutions can be used to construct such illuminations, but are impractical for several reasons. We propose a constructive approach to this problem based on the use of multiple frequencies. The suitable boundary conditions are explicitly constructed and give the desired constraints, provided that a finite number of frequencies, given a priori, are chosen in a fixed range. This method is based on the holomorphicity of the solutions with respect to the frequency and on the regularity theory for the PDE under consideration. This theory finds applications to several hybrid imaging inverse problems, where the unknown coefficients have to be imaged from internal measurements. In order to perform the reconstruction, we often need to find suitable boundary conditions such that the corresponding solutions satisfy certain non-zero constraints, depending on the particular problem under consideration. The multiple frequency approach introduced in this thesis represents a valid alternative to the use of complex geometric optics solutions to construct such boundary conditions. Several examples are discussed.

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Nersesov, Sergey G. "Nonlinear Impulsive and Hybrid Dynamical Systems." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/7147.

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Modern complex dynamical systems typically possess a multiechelon hierarchical hybrid structure characterized by continuous-time dynamics at the lower-level units and logical decision-making units at the higher-level of hierarchy. Hybrid dynamical systems involve an interacting countable collection of dynamical systems defined on subregions of the partitioned state space. Thus, in addition to traditional control systems, hybrid control systems involve supervising controllers which serve to coordinate the (sometimes competing) actions of the lower-level controllers. A subclass of hybrid dynamical systems are impulsive dynamical systems which consist of three elements, namely, a continuous-time differential equation, a difference equation, and a criterion for determining when the states of the system are to be reset. One of the main topics of this dissertation is the development of stability analysis and control design for impulsive dynamical systems. Specifically, we generalize Poincare's theorem to dynamical systems possessing left-continuous flows to address the stability of limit cycles and periodic orbits of left-continuous, hybrid, and impulsive dynamical systems. For nonlinear impulsive dynamical systems, we present partial stability results, that is, stability with respect to part of the system's state. Furthermore, we develop adaptive control framework for general class of impulsive systems as well as energy-based control framework for hybrid port-controlled Hamiltonian systems. Extensions of stability theory for impulsive dynamical systems with respect to the nonnegative orthant of the state space are also addressed in this dissertation. Furthermore, we design optimal output feedback controllers for set-point regulation of linear nonnegative dynamical systems. Another main topic that has been addressed in this research is the stability analysis of large-scale dynamical systems. Specifically, we extend the theory of vector Lyapunov functions by constructing a generalized comparison system whose vector field can be a function of the comparison system states as well as the nonlinear dynamical system states. Furthermore, we present a generalized convergence result which, in the case of a scalar comparison system, specializes to the classical Krasovskii-LaSalle invariant set theorem. Moreover, we develop vector dissipativity theory for large-scale dynamical systems based on vector storage functions and vector supply rates. Finally, using a large-scale dynamical systems perspective, we develop a system-theoretic foundation for thermodynamics. Specifically, using compartmental dynamical system energy flow models, we place the universal energy conservation, energy equipartition, temperature equipartition, and entropy nonconservation laws of thermodynamics on a system-theoretic basis.

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Sessa, Mirko. "An SMT-based framework for the formal analysis of Switched Multi-Domain Kirchhoff Networks." Doctoral thesis, Università degli studi di Trento, 2019. http://hdl.handle.net/11572/243432.

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Many critical systems are based on the combination of components from different physical domains (e.g. mechanical, electrical, hydraulic), and are mathematically modeled as Switched Multi-Domain Kirchhoff Networks (SMDKN). In this thesis, we tackle a major obstacle to formal verification of SMDKN, namely devising a global model amenable to verification in the form of a Hybrid Automaton. This requires the combination of the local dynamics of the components, expressed as Differential Algebraic Equations, according to Kirchhoff's laws, depending on the (exponentially many) operation modes of the network. We propose an automated SMT-based method to analyze networks from multiple physical domains, detecting which modes induce invalid (i.e. inconsistent) constraints, and to produce a Hybrid Automaton model that accurately describes, in terms of Ordinary Differential Equations, the system evolution in the valid modes, catching also the possible non-deterministic behaviors. The experimental evaluation demonstrates that the proposed approach allows several complex multi-domain systems to be formally analyzed and model checked against various system requirements.

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Books on the topic "Hybrid differential equations"

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Geer, James F. A hybrid Pade-Galerkin technique for differential equations. Institute for Computer Applications in Science and Engineeering, 1993.

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Geer, James F. A hybrid perturbation-Galerkin technique for partial differential equations. Institute for Computer Applications in Science and Engineering, 1990.

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1930-, Andersen Carl M., Institute for Computer Applications in Science and Engineering., and Langley Research Center, eds. A hybrid perturbation-Galerkin technique for partial differential equations. NASA Langley Research Center, 1990.

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Hallett, Andrew Hughes. Hybrid algorithms with automatic switching for solving nonlinear equation systems. Dept. of Economics, Fraser of Allander Institute, University of Strathclyde, 1996.

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service), SpringerLink (Online, ed. Nonlinear Hybrid Continuous/Discrete-Time Models. Atlantis Press, 2011.

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1930-, Andersen Carl M., and Langley Research Center, eds. A hybrid perturbation-Galerkin method for differential equations containing a parameter. National Aeronautics and Space Administration, Langley Research Center, 1989.

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1930-, Andersen Carl M., and Langley Research Center, eds. A hybrid perturbation-Galerkin method for differential equations containing a parameter. National Aeronautics and Space Administration, Langley Research Center, 1989.

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Geer, James F. A hybrid perturbation-Galerkin method for differential equations containing a parameter. ICASE, 1989.

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Canada. Dept. of the Environment. Inland Waters. Hybrid Numerical-Analytical Method For the Solution Partial Differential Equations in Ground-Water Modelling. s.n, 1987.

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Kamene͡tskiĭ, V. F. Postroenie gibridnykh skhem na osnove kharakteristicheskikh sootnosheniĭ. Vychislitelʹnyĭ ͡tsentr AN SSSR, 1989.

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Book chapters on the topic "Hybrid differential equations"

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Benchohra, Mouffak, Erdal Karapınar, Jamal Eddine Lazreg, and Abdelkrim Salim. "Hybrid Fractional Differential Equations." In Fractional Differential Equations. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-34877-8_3.

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Liu, Xinzhi, and Kexue Zhang. "Differential Equations on Time Scales." In Impulsive Systems on Hybrid Time Domains. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-06212-5_7.

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Deb, Anish, Srimanti Roychoudhury, and Gautam Sarkar. "Linear Differential Equations." In Analysis and Identification of Time-Invariant Systems, Time-Varying Systems, and Multi-Delay Systems using Orthogonal Hybrid Functions. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-26684-8_6.

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Gallicchio, James, Yong Kiam Tan, Stefan Mitsch, and André Platzer. "Implicit Definitions with Differential Equations for KeYmaera X." In Automated Reasoning. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-10769-6_42.

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AbstractDefinition packages in theorem provers provide users with means of defining and organizing concepts of interest. This system description presents a new definition package for the hybrid systems theorem prover KeYmaera X based on differential dynamic logic (). The package adds KeYmaera X support for user-defined smooth functions whose graphs can be implicitly characterized by formulas. Notably, this makes it possible to implicitly characterize functions, such as the exponential and trigonometric functions, as solutions of differential equations and then prove properties of those functions using ’s differential equation reasoning principles. Trustworthiness of the package is achieved by minimally extending KeYmaera X ’s soundness-critical kernel with a single axiom scheme that expands function occurrences with their implicit characterization. Users are provided with a high-level interface for defining functions and non-soundness-critical tactics that automate low-level reasoning over implicit characterizations in hybrid system proofs.

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Ramos, Carlos, Ana Isabel Santos, and Sandra Vinagre. "The Dynamics of a Hybrid Chaotic System." In Differential and Difference Equations with Applications. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56323-3_48.

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Melliani, Said, K. Hilal, and M. Hannabou. "Existence Results of Hybrid Fractional Integro-Differential Equations." In Recent Advances in Intuitionistic Fuzzy Logic Systems. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-02155-9_17.

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Aouragh, M. Driss. "Uniform Stabilization of a Hybrid System of Elasticity: Riesz Basis Approach." In Differential and Difference Equations with Applications. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-32857-7_9.

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Akhmet, Marat. "The Small Parameter and Differential Equations with Piecewise Constant Argument." In Nonlinear Hybrid Continuous/Discrete-Time Models. Atlantis Press, 2011. http://dx.doi.org/10.2991/978-94-91216-03-9_4.

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Pettersson, Mass Per, Gianluca Iaccarino, and Jan Nordström. "A Hybrid Scheme for Two-Phase Flow." In Polynomial Chaos Methods for Hyperbolic Partial Differential Equations. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10714-1_9.

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Tan, Yong Kiam, and André Platzer. "Deductive Stability Proofs for Ordinary Differential Equations." In Tools and Algorithms for the Construction and Analysis of Systems. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72013-1_10.

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AbstractStability is required for real world controlled systems as it ensures that those systems can tolerate small, real world perturbations around their desired operating states. This paper shows how stability for continuous systems modeled by ordinary differential equations (ODEs) can be formally verified in differential dynamic logic (). The key insight is to specify ODE stability by suitably nesting the dynamic modalities of with first-order logic quantifiers. Elucidating the logical structure of stability properties in this way has three key benefits: i) it provides a flexible means of formally specifying various stability properties of interest, ii) it yields rigorous proofs of those stability properties from ’s axioms with ’s ODE safety and liveness proof principles, and iii) it enables formal analysis of the relationships between various stability properties which, in turn, inform proofs of those properties. These benefits are put into practice through an implementation of stability proofs for several examples in KeYmaera X, a hybrid systems theorem prover based on .

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Conference papers on the topic "Hybrid differential equations"

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Adoghe, Lawrence Osa, Ezekiel Olaoluwa Omole, Luke Azeta Ukpebor, Ola Olayemi Olanegan, Abraham Femi Olanrewaju, and Samuel Olawale Oladimeji. "Hybrid Predictors Methods containing Third Derivatives for Solving Stiff and Non-Stiff First-order Differential Equations." In 2024 International Conference on Science, Engineering and Business for Driving Sustainable Development Goals (SEB4SDG). IEEE, 2024. http://dx.doi.org/10.1109/seb4sdg60871.2024.10629728.

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Omole, Ezekiel Olaoluwa, Ogunware Bankola Gbenga, Florence Dami Ayegbusi, Peter Onu, Tosin Oreyeni, and Kehinde Peter Ajewole. "Hybrid Block Numerical Algorithm for Direct Solutions of Ordinary Differential Equations of the Third and Fourth Orders." In 2024 International Conference on Science, Engineering and Business for Driving Sustainable Development Goals (SEB4SDG). IEEE, 2024. http://dx.doi.org/10.1109/seb4sdg60871.2024.10629770.

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Li, Yabing, Yige Zhao, and Rian Yan. "The existence of solutions for initial value problems of nonlinear fractional hybrid differential equations of variable-order." In 2024 24th International Conference on Control, Automation and Systems (ICCAS). IEEE, 2024. https://doi.org/10.23919/iccas63016.2024.10773276.

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van Beek, D. A., A. Pogromsky, H. Nijmeijer, and J. E. Rooda. "Convex equations and differential inclusions in hybrid systems." In 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601). IEEE, 2004. http://dx.doi.org/10.1109/cdc.2004.1430243.

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Akhadkulov, H., Z. Eshkuvatov, U. A. M. Roslan, and S. Akhatkulov. "On the solutions of fractional hybrid differential equations." In THE 15TH UNIVERSITI MALAYSIA TERENGGANU ANNUAL SYMPOSIUM 2021 (UMTAS 2021). AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0152396.

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Joelianto, E. "Linear impulsive differential equations for hybrid systems modeling." In 2003 European Control Conference (ECC). IEEE, 2003. http://dx.doi.org/10.23919/ecc.2003.7086555.

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Karaseva, T. S. "Identification of Differential Equations Systems With Various Input Effects." In International Workshop “Hybrid methods of modeling and optimization in complex systems”. European Publisher, 2023. http://dx.doi.org/10.15405/epct.23021.19.

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Ken, Yap Lee, and Fudziah Ismail. "Block hybrid-like method for solving delay differential equations." In INTERNATIONAL CONFERENCE ON MATHEMATICS, ENGINEERING AND INDUSTRIAL APPLICATIONS 2014 (ICoMEIA 2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4915663.

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Huang, Yipeng, Ning Guo, Mingoo Seok, Yannis Tsividis, Kyle Mandli, and Simha Sethumadhavan. "Hybrid analog-digital solution of nonlinear partial differential equations." In MICRO-50: The 50th Annual IEEE/ACM International Symposium on Microarchitecture. ACM, 2017. http://dx.doi.org/10.1145/3123939.3124550.

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Zong, Xiaofeng, Fuke Wu, and George Yin. "Stochastic regularization and stabilization of hybrid functional differential equations." In 2015 54th IEEE Conference on Decision and Control (CDC). IEEE, 2015. http://dx.doi.org/10.1109/cdc.2015.7402376.

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Reports on the topic "Hybrid differential equations"

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

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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.

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Abhyankar, Shrirang, Mihai Anitescu, Emil Constantinescu, and Hong Zhang. Efficient Adjoint Computation of Hybrid Systems of Differential Algebraic Equations with Applications in Power Systems. Office of Scientific and Technical Information (OSTI), 2016. http://dx.doi.org/10.2172/1245175.

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