scholarly journals A Class of Non-Linear ODEs with Movable Algebraic Singularities

2012 ◽  
Vol 12 (2) ◽  
pp. 653-667 ◽  
Author(s):  
Thomas Kecker
Keyword(s):  
Non Linear ◽  
Linear Odes ◽  
Algebraic Singularities

scholarly journals Passive control of magneto-nanomaterials transient flow subject to non-linear thermal radiation

2021 ◽  
pp. 169-169
Author(s):  
Ikram Ullah ◽  
Sayed Shah ◽  
Gul Zaman ◽  
Taseer Muhammad ◽  
Zakir Hussain
Keyword(s):  
Thermal Radiation ◽  
Passive Control ◽  
Stretching Sheet ◽  
Transient Flow ◽  
Brownian Diffusion ◽  
Convection Flow ◽  
Stretching Surface ◽  
Surface Drag ◽  
Non Linear ◽  
Linear Odes

Present investigation is concerned with mixed convection flow of Williamson nanoliquid over an unsteady slandering stretching sheet. Aspects of non-linear thermal radiation, Brownian diffusion and thermophoresis effects are addressed. Non-linear stretching surface of varying thickness induce the flow. Novel features of combined zero mass flux and convective conditions are accounted. Use of appropriate transformations results into the non-linear ODEs. Computations for the convergent solutions are provided. Graphs are designed for interpretations to quantities. Nusselt number and surface drag are computationally inspected. Our computed results indicate that attributes of nanoparticles and non-linear thermal radiation enhance the temperature distribution.

scholarly journals Flow* 1.2: More Effective to Play with Hybrid Systems

10.29007/1w4t ◽  
2018 ◽  
Author(s):  
Xin Chen ◽  
Sriram Sankaranarayanan ◽  
Erika Abraham
Keyword(s):  
Hybrid Systems ◽  
Non Linear ◽  
Efficient Scheme ◽  
Linear Odes

This paper gives a brief overview of the new features introduced in the latest version of the tool Flow*. We mainly describe the new efficient scheme for integrating linear ODEs. We show that it can efficiently handle the challenging benchmarks on which, to the best of our knowledge, only SpaceEx works. Moreover, it is also possible to extend the method to deal with unbounded initial sets. A comparison between Flow* 1.2 and SpaceEx on those benchmarks is given. Besides, we also investigate the scalability Flow* 1.2 based on our non-linear line circuit benchmarks.

scholarly journals Non-linear Continuous Systems for Safety Verification

10.29007/w94n ◽  
2018 ◽  
Author(s):  
Andrew Sogokon ◽  
Khalil Ghorbal ◽  
Taylor T Johnson
Keyword(s):  
Differential Equations ◽  
Continuous Systems ◽  
Hybrid Dynamical Systems ◽  
Sat Solving ◽  
Safety Verification ◽  
Linear Polynomial ◽  
Non Linear ◽  
Verification Tools ◽  
Linear Differential ◽  
Linear Odes

Safety verification of hybrid dynamical systems relies crucially on the ability to reason about reachable sets of continuous systems whose evolution is governed by a system of ordinary differential equations (ODEs). Verification tools are often restricted to handling a particular class of continuous systems, such as e.g. differential equations with constant right-hand sides, or systems of affine ODEs. More recently, verification tools capable of working with non-linear differential equations have been developed. The behavior of non-linear systems is known to be in general extremely difficult to analyze because solutions are rarely available in closed-form. In order to assess the practical utility of the various verification tools working with non-linear ODEs it is very useful to maintain a set of verification problems. Similar efforts have been successful in other communities, such as automated theorem proving, SAT solving and numerical analysis, and have accelerated improvements in the tools and their underlying algorithms. We present a set of 65 safety verification problems featuring non-linear polynomial ODEs and for which we have proofs of safety. We discuss the various issues associated with benchmarking the currently available verification tools using these problems.

Inverse Identification of Non-Linear ODEs for the Dynamic Control of Material Testing Systems

2021 ◽  
Author(s):  
Evelyn Lunasin ◽  
Athanasios Iliopoulos ◽  
John Michopoulos ◽  
John Steuben
Keyword(s):  
Dynamic Control ◽  
Material Testing ◽  
Inverse Identification ◽  
Non Linear ◽  
Linear Odes

scholarly journals The Magneto-Natural Convection Flow of a Micropolar Hybrid Nanofluid Over a Vertical Plate Saturated in a Porous Medium

Fluids ◽  
2021 ◽  
Vol 6 (6) ◽  
pp. 202
Author(s):  
A. Mahdy ◽  
E. R. El-Zahar ◽  
A. M. Rashad ◽  
W. Saad ◽  
H. S. Al-Juaydi
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Non Linear ◽  
The Magnetic Field ◽  
Linear Odes

In this study, we investigate the convective flow of a micropolar hybrid nanofluid through a vertical radiating permeable plate in a saturated porous medium. The impact of the presence or absence of the internal heat generation (IHG) in the medium is examined as well as the impacts of the magnetic field and thermal radiation. We apply similarity transformations to the non-dimensionalized equations and render them as a system of non-linear ODEs (Ordinary Differential Equations) subject to appropriate boundary conditions. This system of non-linear ODEs is solved by an adaptive mesh transformation Chebyshev differential quadrature method. The influence of the governing parameters on the temperature, microrotation and velocity is examined. The skin friction coefficient and the Nusselt number are tabulated. We determine that the skin friction coefficient and heat transport rate increase with the increment in the magnetic field. Moreover, the increment in the micropolarity and nanoparticle volume fraction enhances the skin friction coefficient and the Nusselt number. We also conclude that the IHG term improved the flow of the hybrid nanofluid. Finally, our results indicate that employing a hybrid nanofluid increases the heat transfer compared with that in pure water and a nanofluid.

scholarly journals Casson fluid flow with heat and mass transfer in a channel using the differential transform method

2021 ◽  
Vol 49 (1) ◽  
Author(s):  
Asia Yasmin ◽  
◽  
Kashif Ali ◽  
Muhammad Ashraf ◽  
◽  
...  
Keyword(s):  
Mass Transfer ◽  
Fluid Flow ◽  
Heat And Mass Transfer ◽  
Casson Fluid ◽  
Differential Transform Method ◽  
Temperature Fields ◽  
Transform Method ◽  
Differential Transform ◽  
Non Linear ◽  
Linear Odes

In the present investigation, we consider the heat and mass transfer characteristics of steady, incompressible and electrically conducting Casson fluid flow in a channel. The effect of chemical reactions have also been considered. The differential transform method (DTM) is applied to a system of non-linear ODEs, and the results are obtained in the form of DTM series. The principal gain of this approach is that it applies to the non-linear ODEs without requiring any discretization, linearization or perturbation. The velocity, mass and heat transfer profiles thus obtained are in good agreement with those provided by the quasi-linearization method (QLM). Graphical results for velocity, concentration and temperature fields are presented for a certain range of values of the governing parameters.

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