scholarly journals Center boundaries for planar piecewise-smooth differential equations with two zones

2017 ◽  
Vol 445 (1) ◽  
pp. 631-649 ◽  
Author(s):  
Claudio A. Buzzi ◽  
Rubens Pazim ◽  
Set Pérez-González
Keyword(s):  
Differential Equations ◽  
Piecewise Smooth

scholarly journals Limit Cycles of Piecewise Smooth Differential Equations on Two Dimensional Torus

2017 ◽  
Vol 30 (3) ◽  
pp. 1011-1027 ◽  
Author(s):  
Jaume Llibre ◽  
Ricardo Miranda Martins ◽  
Durval José Tonon
Keyword(s):  
Differential Equations ◽  
Limit Cycles ◽  
Piecewise Smooth ◽  
Two Dimensional ◽  
Dimensional Torus

scholarly journals Piecewise smooth solutions of some difference-differential equations

1986 ◽  
Vol 48 (3) ◽  
pp. 262-271 ◽  
Author(s):  
T.N.T Goodman ◽  
I.J Schoenberg ◽  
A Sharma
Keyword(s):  
Differential Equations ◽  
Piecewise Smooth ◽  
Smooth Solutions

scholarly journals Shilnikov chaos, Filippov sliding and boundary equilibrium bifurcations

2018 ◽  
Vol 29 (5) ◽  
pp. 757-777 ◽  
Author(s):  
P. A. GLENDINNING
Keyword(s):  
Differential Equations ◽  
Homoclinic Orbit ◽  
Homoclinic Orbits ◽  
Piecewise Smooth ◽  
Boundary Equilibrium ◽  
The 1960S

In the 1960s, L.P. Shilnikov showed that certain homoclinic orbits for smooth families of differential equations imply the existence of chaos, and there are complicated sequences of bifurcations near the parameter value at which the homoclinic orbit exists. We describe how this analysis is modified if the differential equations are piecewise smooth and the homoclinic orbit has a sliding segment. Moreover, we show that the Shilnikov mechanism appears naturally in the unfolding of boundary equilibrium bifurcations in $\mathbb{R}^3$.

scholarly journals High-accuracy approximation of piecewise smooth functions using the Truncation and Encode approach

2017 ◽  
Vol 2 (2) ◽  
pp. 367-384 ◽  
Author(s):  
Rosa Donat ◽  
Sergio López-Ureña
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Experiments ◽  
High Performance ◽  
Linear Interpolation ◽  
High Accuracy ◽  
Piecewise Smooth ◽  
Approximation Of Functions ◽  
Smooth Functions ◽  
Piecewise Smooth Functions

AbstractIn the present work, we analyze a technique designed by Geraci et al. in [1,11] named the Truncate and Encode (TE) strategy. It was presented as a non-intrusive method for steady and non-steady Partial Differential Equations (PDEs) in Uncertainty Quantification (UQ), and as a weakly intrusive method in the unsteady case.We analyze the TE algorithm applied to the approximation of functions, and in particular its performance for piecewise smooth functions. We carry out some numerical experiments, comparing the performance of the algorithm when using different linear and non-linear interpolation techniques and provide some recommendations that we find useful in order to achieve a high performance of the algorithm.

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