Journal ArticleDOI
Nonlinear heat diffusion simulation using Volterra series expansion
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TLDR
In this article, a method for solving a nonlinear heat diffusion problem based on the use of the Volterra series is presented, which allows splitting naturally the solution as a linear contribution and a non-linear one.About:
This article is published in International Journal of Thermal Sciences.The article was published on 2013-09-01. It has received 12 citations till now. The article focuses on the topics: Volterra series & Volterra integral equation.read more
Citations
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Journal ArticleDOI
Nonlinear thermal system identification using fractional Volterra series
TL;DR: In this article, a new class of nonlinear fractional models based on the Volterra series is proposed for modeling such nonlinear diffusive phenomena, and the models are extended to fractional derivatives, and fractional orthogonal generating functions are used as VOLTERRA kernels.
Sound synthesis of a nonlinear string using Volterra series
David Roze,Thomas Hélie +1 more
TL;DR: In this article, the authors propose to solve and simulate various Kirchhoff models of nonlinear strings thanks to Volterra series, where the string tension is supposed to depend either on the global elongation of the string, or on the local strain located at x.
Journal ArticleDOI
Stability and resonance conditions of second-order fractional systems:
TL;DR: In this paper, the stability and resonance conditions of second-order fractional systems were established in terms of a pseudo-damping factor and a fractional differentiation order, and it was shown numerically that the system root locus presents a discontinuity when the fractional differential order is an integral number.
Journal ArticleDOI
Comparison between the Second and Third Generations of the CRONE Controller: Application to a Thermal Diffusive Interface Medium
TL;DR: Results show that the second generation performs well when the parametric uncertainties do not affect the phase of the plant, whereas the third generation is the most robust, even when both the phase and the gain variations are encountered.
Proceedings ArticleDOI
Fractional Order Sobel Edge Detector
TL;DR: This paper proposes the design of a fractional order Sobel edge detector, and the proposed method is implemented and assessed in the context of road obstacle detection, and contrasted with the conventional Sobeledge detector.
References
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Journal ArticleDOI
A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting
TL;DR: In this paper, the modified (underrelaxed, damped) Newton method is extended in such a way as to apply to the solution of ill-conditioned systems of nonlinear equations, i.e. systems having a "nearly singular" Jacobian at some iterate.
Journal ArticleDOI
Analytical Foundations of Volterra Series
TL;DR: In this paper, the authors study the analysis involved with Volterra series operators, and prove a general Steady-state theorem for the spectrum of the output of a VOLTERRA series operator in terms of a periodic input.
Journal ArticleDOI
Sound synthesis of a nonlinear string using Volterra series
Thomas Hélie,David Roze +1 more
TL;DR: In this paper, the authors propose to solve and simulate various Kirchhoff models of nonlinear strings using Volterra series, where the boundary conditions are simple Dirichlet homogeneous ones or general dynamic conditions (allowing the string to be connected to any system).
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An adaptive Huber method for weakly singular second kind Volterra integral equations with non-linear dependencies between unknowns and their integrals
Time-domain analysis of nonlinear systems with finite number of continuous derivatives
Ibrahim N. Hajj,S. Skelboe +1 more