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Existence of solutions to equations for the flow of an incompressible fluid with capillary effects
High order product integration methods for a Volterra integral equation with logarithmic singular kernel
1. | Centro de Matematica e Aplicącoes, Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal |
2. | Laboratorio Interdisciplinar de Computacao Cientıfica, Faculdades COC, 14096-160 Ribeirao Preto - SP, Brazil |
3. | Centro de Matemática Aplicacoes, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal |
[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] |
Oleksandr Boichuk, Victor Feruk. Boundary-value problems for weakly singular integral equations. Discrete and Continuous Dynamical Systems - B, 2022, 27 (3) : 1379-1395. doi: 10.3934/dcdsb.2021094 |
[4] |
Hermann Brunner. The numerical solution of weakly singular Volterra functional integro-differential equations with variable delays. Communications on Pure and Applied Analysis, 2006, 5 (2) : 261-276. doi: 10.3934/cpaa.2006.5.261 |
[5] |
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 |
[6] |
Diogo A. Gomes, Gabriele Terrone. Bernstein estimates: weakly coupled systems and integral equations. Communications on Pure and Applied Analysis, 2012, 11 (3) : 861-883. doi: 10.3934/cpaa.2012.11.861 |
[7] |
M. R. Arias, R. Benítez. Properties of solutions for nonlinear Volterra integral equations. Conference Publications, 2003, 2003 (Special) : 42-47. doi: 10.3934/proc.2003.2003.42 |
[8] |
Philipp Bader, Sergio Blanes, Fernando Casas, Mechthild Thalhammer. Efficient time integration methods for Gross-Pitaevskii equations with rotation term. Journal of Computational Dynamics, 2019, 6 (2) : 147-169. doi: 10.3934/jcd.2019008 |
[9] |
Patricia J.Y. Wong. Existence of solutions to singular integral equations. Conference Publications, 2009, 2009 (Special) : 818-827. doi: 10.3934/proc.2009.2009.818 |
[10] |
Yufeng Shi, Tianxiao Wang, Jiongmin Yong. Mean-field backward stochastic Volterra integral equations. Discrete and Continuous Dynamical Systems - B, 2013, 18 (7) : 1929-1967. doi: 10.3934/dcdsb.2013.18.1929 |
[11] |
Onur Alp İlhan. Solvability of some volterra type integral equations in hilbert space. Conference Publications, 2007, 2007 (Special) : 28-34. doi: 10.3934/proc.2007.2007.28 |
[12] |
Tianxiao Wang, Yufeng Shi. Symmetrical solutions of backward stochastic Volterra integral equations and their applications. Discrete and Continuous Dynamical Systems - B, 2010, 14 (1) : 251-274. doi: 10.3934/dcdsb.2010.14.251 |
[13] |
Yufeng Shi, Tianxiao Wang, Jiongmin Yong. Optimal control problems of forward-backward stochastic Volterra integral equations. Mathematical Control and Related Fields, 2015, 5 (3) : 613-649. doi: 10.3934/mcrf.2015.5.613 |
[14] |
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 |
[15] |
Xiaohui Yu. Liouville type theorems for singular integral equations and integral systems. Communications on Pure and Applied Analysis, 2016, 15 (5) : 1825-1840. doi: 10.3934/cpaa.2016017 |
[16] |
Valentina Casarino, Paolo Ciatti, Silvia Secco. Product structures and fractional integration along curves in the space. Discrete and Continuous Dynamical Systems - S, 2013, 6 (3) : 619-635. doi: 10.3934/dcdss.2013.6.619 |
[17] |
Lili Ju, Xinfeng Liu, Wei Leng. Compact implicit integration factor methods for a family of semilinear fourth-order parabolic equations. Discrete and Continuous Dynamical Systems - B, 2014, 19 (6) : 1667-1687. doi: 10.3934/dcdsb.2014.19.1667 |
[18] |
Claudio Marchi. On the convergence of singular perturbations of Hamilton-Jacobi equations. Communications on Pure and Applied Analysis, 2010, 9 (5) : 1363-1377. doi: 10.3934/cpaa.2010.9.1363 |
[19] |
Yushi Hamaguchi. Extended backward stochastic Volterra integral equations and their applications to time-Inconsistent stochastic recursive control problems. Mathematical Control and Related Fields, 2021, 11 (2) : 433-478. doi: 10.3934/mcrf.2020043 |
[20] |
Ludger Overbeck, Jasmin A. L. Röder. Path-dependent backward stochastic Volterra integral equations with jumps, differentiability and duality principle. Probability, Uncertainty and Quantitative Risk, 2018, 3 (0) : 4-. doi: 10.1186/s41546-018-0030-2 |
2021 Impact Factor: 1.273
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