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A fast iterative scheme for variational inclusions
Approximating the basin of attraction of timeperiodic ODEs by meshless collocation of a Cauchy problem
1.  Department of Mathematics, University of Sussex, Brighton, BN1 9RF 
[1] 
Peter Giesl, James McMichen. Determination of the basin of attraction of a periodic orbit in two dimensions using meshless collocation. Journal of Computational Dynamics, 2016, 3 (2) : 191210. doi: 10.3934/jcd.2016010 
[2] 
Peter Giesl, Holger Wendland. Approximating the basin of attraction of timeperiodic ODEs by meshless collocation. Discrete & Continuous Dynamical Systems, 2009, 25 (4) : 12491274. doi: 10.3934/dcds.2009.25.1249 
[3] 
Ábel Garab. Unique periodic orbits of a delay differential equation with piecewise linear feedback function. Discrete & Continuous Dynamical Systems, 2013, 33 (6) : 23692387. doi: 10.3934/dcds.2013.33.2369 
[4] 
Peter Giesl. Construction of a finitetime Lyapunov function by meshless collocation. Discrete & Continuous Dynamical Systems  B, 2012, 17 (7) : 23872412. doi: 10.3934/dcdsb.2012.17.2387 
[5] 
Hjörtur Björnsson, Sigurdur Hafstein, Peter Giesl, Enrico Scalas, Skuli Gudmundsson. Computation of the stochastic basin of attraction by rigorous construction of a Lyapunov function. Discrete & Continuous Dynamical Systems  B, 2019, 24 (8) : 42474269. doi: 10.3934/dcdsb.2019080 
[6] 
Peter Giesl. Construction of a global Lyapunov function using radial basis functions with a single operator. Discrete & Continuous Dynamical Systems  B, 2007, 7 (1) : 101124. doi: 10.3934/dcdsb.2007.7.101 
[7] 
Martin D. Buhmann, Slawomir Dinew. Limits of radial basis function interpolants. Communications on Pure & Applied Analysis, 2007, 6 (3) : 569585. doi: 10.3934/cpaa.2007.6.569 
[8] 
Peter Giesl. Necessary condition for the basin of attraction of a periodic orbit in nonsmooth periodic systems. Discrete & Continuous Dynamical Systems, 2007, 18 (2&3) : 355373. doi: 10.3934/dcds.2007.18.355 
[9] 
Antonio Cañada, Salvador Villegas. Lyapunov inequalities for partial differential equations at radial higher eigenvalues. Discrete & Continuous Dynamical Systems, 2013, 33 (1) : 111122. doi: 10.3934/dcds.2013.33.111 
[10] 
Anatoli F. Ivanov, Sergei Trofimchuk. Periodic solutions and their stability of a differentialdifference equation. Conference Publications, 2009, 2009 (Special) : 385393. doi: 10.3934/proc.2009.2009.385 
[11] 
P. Dormayer, A. F. Ivanov. Symmetric periodic solutions of a delay differential equation. Conference Publications, 1998, 1998 (Special) : 220230. doi: 10.3934/proc.1998.1998.220 
[12] 
Robert Baier, Lars Grüne, Sigurđur Freyr Hafstein. Linear programming based Lyapunov function computation for differential inclusions. Discrete & Continuous Dynamical Systems  B, 2012, 17 (1) : 3356. doi: 10.3934/dcdsb.2012.17.33 
[13] 
Imtiaz Ahmad, SirajulIslam, Mehnaz, Sakhi Zaman. Local meshless differential quadrature collocation method for timefractional PDEs. Discrete & Continuous Dynamical Systems  S, 2020, 13 (10) : 26412654. doi: 10.3934/dcdss.2020223 
[14] 
Nguyen Thieu Huy, Ngo Quy Dang. Dichotomy and periodic solutions to partial functional differential equations. Discrete & Continuous Dynamical Systems  B, 2017, 22 (8) : 31273144. doi: 10.3934/dcdsb.2017167 
[15] 
Chunhua Jin, Jingxue Yin, Zejia Wang. Positive periodic solutions to a nonlinear fourthorder differential equation. Communications on Pure & Applied Analysis, 2008, 7 (5) : 12251235. doi: 10.3934/cpaa.2008.7.1225 
[16] 
Sigurdur Hafstein, Skuli Gudmundsson, Peter Giesl, Enrico Scalas. Lyapunov function computation for autonomous linear stochastic differential equations using sumofsquares programming. Discrete & Continuous Dynamical Systems  B, 2018, 23 (2) : 939956. doi: 10.3934/dcdsb.2018049 
[17] 
Xiao Wang, Zhaohui Yang, Xiongwei Liu. Periodic and almost periodic oscillations in a delay differential equation system with timevarying coefficients. Discrete & Continuous Dynamical Systems, 2017, 37 (12) : 61236138. doi: 10.3934/dcds.2017263 
[18] 
Avner Friedman, Harsh Vardhan Jain. A partial differential equation model of metastasized prostatic cancer. Mathematical Biosciences & Engineering, 2013, 10 (3) : 591608. doi: 10.3934/mbe.2013.10.591 
[19] 
Hernán R. Henríquez, Claudio Cuevas, Alejandro Caicedo. Asymptotically periodic solutions of neutral partial differential equations with infinite delay. Communications on Pure & Applied Analysis, 2013, 12 (5) : 20312068. doi: 10.3934/cpaa.2013.12.2031 
[20] 
Meina Gao, Jianjun Liu. A degenerate KAM theorem for partial differential equations with periodic boundary conditions. Discrete & Continuous Dynamical Systems, 2020, 40 (10) : 59115928. doi: 10.3934/dcds.2020252 
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