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Fast numerical collocation solutions of integral equations
1. | Department of Scientific Computing and Computer Applications, Sun Yat-sen University, Guangzhou 510275, China, China |
2. | Department of Mathematics, Syracuse University, Syracuse, NY 13244-1150, United States |
[1] |
Yin Yang, Yunqing Huang. Spectral Jacobi-Galerkin methods and iterated methods for Fredholm integral equations of the second kind with weakly singular kernel. Discrete and Continuous Dynamical Systems - S, 2019, 12 (3) : 685-702. 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 and Applied Analysis, 2006, 5 (2) : 395-413. doi: 10.3934/cpaa.2006.5.395 |
[3] |
Hui Liang, Hermann Brunner. Collocation methods for differential equations with piecewise linear delays. Communications on Pure and Applied Analysis, 2012, 11 (5) : 1839-1857. doi: 10.3934/cpaa.2012.11.1839 |
[4] |
Lijian Jiang, Yalchin Efendiev, Victor Ginting. Multiscale methods for parabolic equations with continuum spatial scales. Discrete and Continuous Dynamical Systems - B, 2007, 8 (4) : 833-859. doi: 10.3934/dcdsb.2007.8.833 |
[5] |
Angelamaria Cardone, Dajana Conte, Beatrice Paternoster. Two-step collocation methods for fractional differential equations. Discrete and Continuous Dynamical Systems - B, 2018, 23 (7) : 2709-2725. 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 and Continuous Dynamical Systems - S, 2016, 9 (1) : 33-42. doi: 10.3934/dcdss.2016.9.33 |
[7] |
Jean Dolbeault, Giuseppe Toscani. Fast diffusion equations: Matching large time asymptotics by relative entropy methods. Kinetic and Related Models, 2011, 4 (3) : 701-716. doi: 10.3934/krm.2011.4.701 |
[8] |
Hong Wang, Aijie Cheng, Kaixin Wang. Fast finite volume methods for space-fractional diffusion equations. Discrete and Continuous Dynamical Systems - B, 2015, 20 (5) : 1427-1441. doi: 10.3934/dcdsb.2015.20.1427 |
[9] |
Assyr Abdulle. Multiscale methods for advection-diffusion problems. Conference Publications, 2005, 2005 (Special) : 11-21. doi: 10.3934/proc.2005.2005.11 |
[10] |
Alexander Mielke. Weak-convergence methods for Hamiltonian multiscale problems. Discrete and Continuous Dynamical Systems, 2008, 20 (1) : 53-79. doi: 10.3934/dcds.2008.20.53 |
[11] |
Juan Wen, Yaling He, Yinnian He, Kun Wang. Stabilized finite element methods based on multiscale enrichment for Allen-Cahn and Cahn-Hilliard equations. Communications on Pure and Applied Analysis, 2022, 21 (6) : 1873-1894. doi: 10.3934/cpaa.2021074 |
[12] |
Giulia Bertaglia, Liu Liu, Lorenzo Pareschi, Xueyu Zhu. Bi-fidelity stochastic collocation methods for epidemic transport models with uncertainties. Networks and Heterogeneous Media, 2022, 17 (3) : 401-425. doi: 10.3934/nhm.2022013 |
[13] |
Z. K. Eshkuvatov, M. Kammuji, Bachok M. Taib, N. M. A. Nik Long. Effective approximation method for solving linear Fredholm-Volterra integral equations. Numerical Algebra, Control and Optimization, 2017, 7 (1) : 77-88. doi: 10.3934/naco.2017004 |
[14] |
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 and Related Models, 2017, 10 (1) : 61-91. doi: 10.3934/krm.2017003 |
[15] |
Juan Campos, Rafael Obaya, Massimo Tarallo. Favard theory and fredholm alternative for disconjugate recurrent second order equations. Communications on Pure and Applied Analysis, 2017, 16 (4) : 1199-1232. doi: 10.3934/cpaa.2017059 |
[16] |
Yoonsang Lee, Bjorn Engquist. Variable step size multiscale methods for stiff and highly oscillatory dynamical systems. Discrete and Continuous Dynamical Systems, 2014, 34 (3) : 1079-1097. doi: 10.3934/dcds.2014.34.1079 |
[17] |
Dajana Conte, Raffaele D'Ambrosio, Beatrice Paternoster. On the stability of $\vartheta$-methods for stochastic Volterra integral equations. Discrete and Continuous Dynamical Systems - B, 2018, 23 (7) : 2695-2708. doi: 10.3934/dcdsb.2018087 |
[18] |
Wenxiong Chen, Shijie Qi. Direct methods on fractional equations. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 1269-1310. doi: 10.3934/dcds.2019055 |
[19] |
Martino Bardi, Annalisa Cesaroni, Daria Ghilli. Large deviations for some fast stochastic volatility models by viscosity methods. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 3965-3988. doi: 10.3934/dcds.2015.35.3965 |
[20] |
B. S. Goh, W. J. Leong, Z. Siri. Partial Newton methods for a system of equations. Numerical Algebra, Control and Optimization, 2013, 3 (3) : 463-469. doi: 10.3934/naco.2013.3.463 |
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