Renormalization group second‐order approximation for singularly perturbed nonlinear ordinary differential equations
Sign Up to like & getrecommendations! Published in 2018 at "Mathematical Methods in The Applied Sciences"
DOI: 10.1002/mma.5107
Abstract: Abstract]We consider a two time scale nonlinear system of ordinary differential equations. The small parameter of the system is the ratio ε of the time scales. We search for an approximation involving only the slow… read more here.
Keywords: ordinary differential; order; order approximation; time ... See more keywords
On the applications of neural ordinary differential equations in medical image analysis
Sign Up to like & getrecommendations! Published in 2024 at "Artificial Intelligence Review"
DOI: 10.1007/s10462-024-10894-0
Abstract: Medical image analysis tasks are characterized by high-noise, volumetric, and multi-modality, posing challenges for the model that attempts to learn robust features from the input images. Over the last decade, deep neural networks (DNNs) have… read more here.
Keywords: image analysis; model; medical image; ordinary differential ... See more keywords
Mean-square convergence of numerical methods for random ordinary differential equations
Sign Up to like & getrecommendations! Published in 2020 at "Numerical Algorithms"
DOI: 10.1007/s11075-020-00967-w
Abstract: The aim of this work is to analyze the mean-square convergence rates of numerical schemes for random ordinary differential equations (RODEs). First, a relation between the global and local mean-square convergence order of one-step explicit… read more here.
Keywords: ordinary differential; random ordinary; square convergence; mean square ... See more keywords
Solvability of Linear Boundary-Value Problems for Ordinary Differential Systems in the Space CN
Sign Up to like & getrecommendations! Published in 2024 at "Ukrainian Mathematical Journal"
DOI: 10.1007/s11253-025-02451-x
Abstract: We study linear boundary-value problems for systems of the first-order ordinary differential equations with the most general boundary conditions in the normed spaces of continuously differentiable functions on a finite closed interval. The boundary conditions… read more here.
Keywords: ordinary differential; linear boundary; solvability linear; boundary value ... See more keywords
Asymptotically efficient parameter estimation for ordinary differential equations
Sign Up to like & getrecommendations! Published in 2017 at "Science China Mathematics"
DOI: 10.1007/s11425-017-9155-0
Abstract: Parameter estimation for ordinary differential equations arises in many fields of science and engineering. To be the best of our knowledge, traditional methods are often either computationally intensive or inaccurate for statistical inference. Ramsay et… read more here.
Keywords: estimation ordinary; parameter estimation; ordinary differential; differential equations ... See more keywords
High-Order Methods for Systems of Fractional Ordinary Differential Equations and Their Application to Time-Fractional Diffusion Equations
Sign Up to like & getrecommendations! Published in 2021 at "Mathematics in Computer Science"
DOI: 10.1007/s11786-019-00448-x
Abstract: Taking into account the regularity properties of the solutions of fractional differential equations, we develop a numerical method which is able to deal, with the same accuracy, with both smooth and nonsmooth solutions of systems… read more here.
Keywords: ordinary differential; fractional diffusion; time fractional; systems fractional ... See more keywords
Solving Quaternion Ordinary Differential Equations with Two-Sided Coefficients
Sign Up to like & getrecommendations! Published in 2018 at "Qualitative Theory of Dynamical Systems"
DOI: 10.1007/s12346-017-0246-z
Abstract: The theory of quaternion differential equations (QDEs) has recently received a lot of attention. They have numerous applications in physics and engineering problems. In the present investigation, a new approach to solve the linear QDEs… read more here.
Keywords: ordinary differential; two sided; sided coefficients; differential equations ... See more keywords
On Gauge Transforms of Autonomous Ordinary Differential Equations
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DOI: 10.1007/s12346-025-01416-6
Abstract: The notion of gauge transform has its origin in Physics (Field Theory). In the present note we discuss – from a purely mathematical perspective – special gauge transforms of autonomous first order ODE’s and their… read more here.
Keywords: differential equations; ordinary differential; transforms autonomous; autonomous ordinary ... See more keywords
A Class of Hybrid Methods for Direct Integration of Fourth-Order Ordinary Differential Equations
Sign Up to like & getrecommendations! Published in 2017 at "Bulletin of the Malaysian Mathematical Sciences Society"
DOI: 10.1007/s40840-017-0520-x
Abstract: A class of hybrid methods for solving fourth-order ordinary differential equations (HMFD) is proposed and investigated. Using the theory of B-series, we study the order of convergence of the HMFD methods. The main result is… read more here.
Keywords: ordinary differential; order; order ordinary; fourth order ... See more keywords
A new ordinary differential equation for the evaluation of the frequency-domain Green function
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DOI: 10.1016/j.apor.2019.03.003
Abstract: Abstract Clement (2013) derived a second order ordinary differential equation (ODE) satisfied by the free-surface Green function in the frequency domain. Since then, similar ODEs for the gradient of the Green function have been developed.… read more here.
Keywords: differential equation; green function; ordinary differential; frequency domain ... See more keywords
Thermal resistance capacity model for short-term borehole heat exchanger simulation with non-stiff ordinary differential equations
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DOI: 10.1016/j.geothermics.2017.06.011
Abstract: Abstract In the present study, a new thermal resistance capacity circuit for the heat transfer modeling in borehole heat exchanger with low computation time is developed. Generally, the thermal circuit models result in sets of… read more here.
Keywords: ordinary differential; thermal resistance; model; resistance capacity ... See more keywords