1 |
P. Baratella and A. Orsi, A new approach to the numerical solution of weakly singular Volterra integral equations, J. Comput. Appl. Math. 163 (2004), no. 2, 401-418.
DOI
|
2 |
C. Canuto, M. Y. Hussaini, and A. Quarteroni, Spectral Methods, Fundamentals in single domains, Sci. Comput., Springer-Verlag, Berlin, 2006
|
3 |
Y. Chen and T. Tang, Spectral methods for weakly singular Volterra integral equations with smooth solutions, J. Comput. Appl. Math. 233 (2009), no. 4, 938-950.
DOI
|
4 |
Y. Chen and T. Tang, Convergence analysis of the Jacobi spectral-collocation methods for Volterra integral equation with a weakly singular kernel, Math. Comp. 79 (2010), no. 269, 147-167.
DOI
|
5 |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Appl. Math. Sci., Springer-Verlag, Heidelberg, 2nd Edition, 1998.
|
6 |
J. Douglas, T. Dupont, and L. Wahlbin, The stability in of the -projection into finite element function spaces, Numer. Math. 23 (1974), no. 3, 193-197.
DOI
|
7 |
D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer-Verlag, 1981.
|
8 |
A. Kufner and L. E. Persson, Weighted Inequalities of Hardy Type, World Scientific, New York, 2003.
|
9 |
G. Mastroianni and D. Occorsto, Optimal systems of nodes for Lagrange interpolation on bounded intervals: a survey, J. Comput. Appl. Math. 134 (2001), no. 1-2, 325-341.
DOI
|
10 |
P. Nevai, Mean convergence of Lagrange interpolation: III, Trans. Amer. Math. Soc. 282 (1984), no. 2, 669-698.
DOI
|
11 |
D. L. Ragozin, Polynomial approximation on compact manifolds and homogeneous spaces, Trans. Amer. Math. Soc. 150 (1970), 41-53.
DOI
|
12 |
D. L. Ragozin, Constructive polynomial approximation on spheres and projective spaces, Trans. Amer. Math. Soc. 162 (1971), 157-170.
|
13 |
S. Jie, T. Tao, and L. Wang, Spectral methods. Algorithms, analysis and applications, Springer Ser. Comput. Math., 41. Springer, Heidelberg, 2011.
|
14 |
T. Tang, X. Xu, and J. Cheng. On Spectral methods for Volterra integral equation and the convergence analysis, J. Comput. Math. 26 (2008), no. 6, 825-837.
|
15 |
X. Tao, Z. Xie, and X. Zhou, Spectral Petrov-Galerkin methods for the second kind Volterra type integro-differential equations, Numer. Math. Theory Methods Appl. 4 (2011), no. 2, 216-236.
|
16 |
Z. Wan, Y. Chen, and Y. Huang, Legendre spectral Galerkin method for second-kind Volterra integral equations, Front. Math. China 4 (2009), no. 1, 181-193.
DOI
|
17 |
Y. Wei and Y. Chen, Convergence analysis of the spectral methods for weakly singular Volterra integro-differential equations with smooth solutions, Adv. Appl. Math. Mech. 4 (2012), no. 1, 1-20.
DOI
|
18 |
Y. Yang, Y. Chen, and Y. Huang, Convergence analysis of Legendre-collocation methods for nonlinear Volterra type integro equations, Adv. Appl. Math. Mech. 7 (2015), no. 1, 74-88.
DOI
|
19 |
Z. Xie and X. Li, and T. Tang, Convergence analysis of spectral Galerkin methods for Volterra type integral equations, J. Sci. Comput. 53 (2012), no. 2, 414-434.
DOI
|
20 |
Y. Yang, Y. Chen, and Y. Huang, Convergence analysis of the Jacobi spectral-collocation method for fractional integro-differential equations, Acta Math. Sci. Ser. B Engl. Ed. 34 (2014), no. 3, 673-690.
|