Autonomous Second-Order ODEs: A Geometric Approach
AxiomsGiven an autonomous second-order ordinary differential equation (ODE), we define a Riemannian metric on an open subset of the first-order jet bundle. A relationship is established between the solutions of the ODE and the geodesic curves with respect to ...
Antonio J. Pan-Collantes +1 more
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Elzaki Transform Method for Natural Frequency Analysis of Euler-Bernoulli Beams [PDF]
Engineering and Technology Journal, 2023 Free vibration analysis of thin beams under dynamic excitation is important in design to prevent resonance failures that occur when the excitation frequency coincides with the natural vibration frequency.
Charles Ike, Tarig Elzaki
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Exact ODE Framework for Classical and Quantum Corrections for the Lennard-Jones Second Virial Coefficient [PDF]
EntropyYanmei Li +2 more
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Results in Physics, 2023 The Lie symmetry analysis of the Riabouchinsky Proudman Johnson (RPJ) equation is discussed in this research. In the onset, we derive the geometric vector fields using the classical Lie symmetry technique. Here, we have a four-dimensional Lie algebra.
A. Hussain +3 more
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Evaluations of series of the $q$-Watson, $q$-Dixon, and $q$-Whipple type [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 Using $q$-series identities and series rearrangement, we establish several extensions of $q$-Watson formulas with two extra integer parameters. Then they and Sears' transformation formula are utilized to derive some generalizations of $q$-Dixon formulas ...
Chuanan Wei, Xiaoxia Wang
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Carleman linearization approach for chemical kinetics integration toward quantum computation
Scientific Reports, 2023 The Harrow, Hassidim, Lloyd (HHL) algorithm, known as the pioneering algorithm for solving linear equations in quantum computers, is expected to accelerate solving large-scale linear ordinary differential equations (ODEs).
Takaki Akiba, Youhi Morii, Kaoru Maruta
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A Universal Ordinary Differential Equation [PDF]
Logical Methods in Computer Science, 2020 An astonishing fact was established by Lee A. Rubel (1981): there exists a fixed non-trivial fourth-order polynomial differential algebraic equation (DAE) such that for any positive continuous function $\varphi$ on the reals, and for any positive ...
Olivier Bournez, Amaury Pouly
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Exploration of the Significance of Autocatalytic Chemical Reaction and Cattaneo-Christov Heat Flux on the Dynamics of a Micropolar Fluid [PDF]
Journal of Applied and Computational Mechanics, 2020 During the homogeneous-heterogeneous autocatalytic chemical reaction in the dynamics of micropolar fluid, relaxation of heat transfer is inevitable; hence Cattaneo-Christov heat flux model is investigated in this report.
G. Sarojamma +3 more
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The Structure of Differential Invariants and Differential Cut Elimination [PDF]
Logical Methods in Computer Science, 2012 The biggest challenge in hybrid systems verification is the handling of differential equations. Because computable closed-form solutions only exist for very simple differential equations, proof certificates have been proposed for more scalable ...
Andre Platzer
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WKB analysis of the linear problem for modified affine Toda field equations
Journal of High Energy Physics, 2023 We study the WKB analysis of the solutions to the linear problem for a modified affine Toda field equation, which is equivalent to the higher-order ordinary differential equation (ODE) studied in the ODE/IM correspondence.
Katsushi Ito, Mingshuo Zhu
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