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Fast numerical collocation solutions of integral equations
1.  Department of Scientific Computing and Computer Applications, Sun Yatsen University, Guangzhou 510275, China, China 
2.  Department of Mathematics, Syracuse University, Syracuse, NY 132441150, United States 
[1] 
Yin Yang, Yunqing Huang. Spectral JacobiGalerkin methods and iterated methods for Fredholm integral equations of the second kind with weakly singular kernel. Discrete & Continuous Dynamical Systems  S, 2019, 12 (3) : 685702. doi: 10.3934/dcdss.2019043 
[2] 
A. Pedas, G. Vainikko. Smoothing transformation and piecewise polynomial projection methods for weakly singular Fredholm integral equations. Communications on Pure & Applied Analysis, 2006, 5 (2) : 395413. doi: 10.3934/cpaa.2006.5.395 
[3] 
Hui Liang, Hermann Brunner. Collocation methods for differential equations with piecewise linear delays. Communications on Pure & Applied Analysis, 2012, 11 (5) : 18391857. doi: 10.3934/cpaa.2012.11.1839 
[4] 
Lijian Jiang, Yalchin Efendiev, Victor Ginting. Multiscale methods for parabolic equations with continuum spatial scales. Discrete & Continuous Dynamical Systems  B, 2007, 8 (4) : 833859. doi: 10.3934/dcdsb.2007.8.833 
[5] 
Angelamaria Cardone, Dajana Conte, Beatrice Paternoster. Twostep collocation methods for fractional differential equations. Discrete & Continuous Dynamical Systems  B, 2018, 23 (7) : 27092725. doi: 10.3934/dcdsb.2018088 
[6] 
Ferdinando Auricchio, Lourenco Beirão da Veiga, Josef Kiendl, Carlo Lovadina, Alessandro Reali. Isogeometric collocation mixed methods for rods. Discrete & Continuous Dynamical Systems  S, 2016, 9 (1) : 3342. doi: 10.3934/dcdss.2016.9.33 
[7] 
Jean Dolbeault, Giuseppe Toscani. Fast diffusion equations: Matching large time asymptotics by relative entropy methods. Kinetic & Related Models, 2011, 4 (3) : 701716. doi: 10.3934/krm.2011.4.701 
[8] 
Hong Wang, Aijie Cheng, Kaixin Wang. Fast finite volume methods for spacefractional diffusion equations. Discrete & Continuous Dynamical Systems  B, 2015, 20 (5) : 14271441. doi: 10.3934/dcdsb.2015.20.1427 
[9] 
Assyr Abdulle. Multiscale methods for advectiondiffusion problems. Conference Publications, 2005, 2005 (Special) : 1121. doi: 10.3934/proc.2005.2005.11 
[10] 
Alexander Mielke. Weakconvergence methods for Hamiltonian multiscale problems. Discrete & Continuous Dynamical Systems  A, 2008, 20 (1) : 5379. doi: 10.3934/dcds.2008.20.53 
[11] 
Matteo Bonforte, Jean Dolbeault, Matteo Muratori, Bruno Nazaret. Weighted fast diffusion equations (Part Ⅱ): Sharp asymptotic rates of convergence in relative error by entropy methods. Kinetic & Related Models, 2017, 10 (1) : 6191. doi: 10.3934/krm.2017003 
[12] 
Z. K. Eshkuvatov, M. Kammuji, Bachok M. Taib, N. M. A. Nik Long. Effective approximation method for solving linear FredholmVolterra integral equations. Numerical Algebra, Control & Optimization, 2017, 7 (1) : 7788. doi: 10.3934/naco.2017004 
[13] 
Juan Campos, Rafael Obaya, Massimo Tarallo. Favard theory and fredholm alternative for disconjugate recurrent second order equations. Communications on Pure & Applied Analysis, 2017, 16 (4) : 11991232. doi: 10.3934/cpaa.2017059 
[14] 
Wenxiong Chen, Shijie Qi. Direct methods on fractional equations. Discrete & Continuous Dynamical Systems  A, 2019, 39 (3) : 12691310. doi: 10.3934/dcds.2019055 
[15] 
Dajana Conte, Raffaele D'Ambrosio, Beatrice Paternoster. On the stability of $\vartheta$methods for stochastic Volterra integral equations. Discrete & Continuous Dynamical Systems  B, 2018, 23 (7) : 26952708. doi: 10.3934/dcdsb.2018087 
[16] 
Yoonsang Lee, Bjorn Engquist. Variable step size multiscale methods for stiff and highly oscillatory dynamical systems. Discrete & Continuous Dynamical Systems  A, 2014, 34 (3) : 10791097. doi: 10.3934/dcds.2014.34.1079 
[17] 
Martino Bardi, Annalisa Cesaroni, Daria Ghilli. Large deviations for some fast stochastic volatility models by viscosity methods. Discrete & Continuous Dynamical Systems  A, 2015, 35 (9) : 39653988. doi: 10.3934/dcds.2015.35.3965 
[18] 
B. S. Goh, W. J. Leong, Z. Siri. Partial Newton methods for a system of equations. Numerical Algebra, Control & Optimization, 2013, 3 (3) : 463469. doi: 10.3934/naco.2013.3.463 
[19] 
Richard A. Norton, G. R. W. Quispel. Discrete gradient methods for preserving a first integral of an ordinary differential equation. Discrete & Continuous Dynamical Systems  A, 2014, 34 (3) : 11471170. doi: 10.3934/dcds.2014.34.1147 
[20] 
Dorina Mitrea and Marius Mitrea. Boundary integral methods for harmonic differential forms in Lipschitz domains. Electronic Research Announcements, 1996, 2: 9297. 
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