Modified asymptotic orders of the direct Filon method for a class of Volterra integral equations
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[1] P. Davis. Interpolation and approximation , 1965 .
[2] Qinghua Wu,et al. On graded meshes for weakly singular Volterra integral equations with oscillatory trigonometric kernels , 2014, J. Comput. Appl. Math..
[3] Shuhuang Xiang,et al. On the convergence rates of Filon methods for the solution of a Volterra integral equation with a highly oscillatory Bessel kernel , 2013, Appl. Math. Lett..
[4] Shuhuang Xiang,et al. Efficient Filon-type methods for (∫abf(x), eiωg(x), dx) , 2007, Numerische Mathematik.
[5] J. Klafter,et al. The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .
[6] A. Iserles. On the numerical quadrature of highly‐oscillating integrals I: Fourier transforms , 2004 .
[7] Alexander G. Ramm,et al. Theory and Applications of Some New Classes of Integral Equations , 1980 .
[8] Shuhuang Xiang,et al. Clenshaw–Curtis–Filon-type methods for highly oscillatory Bessel transforms and applications , 2011 .
[9] Hermann Brunner,et al. Discontinuous Galerkin approximations for Volterra integral equations of the first kind , 2009 .
[10] Sheehan Olver,et al. Numerical approximation of vector-valued highly oscillatory integrals , 2007 .
[11] S. Xiang. Efficient Filon-type methods for $$\int_a^bf(x)\,{\rm e}^{{\rm i}\omega g(x)}\,{\rm d}x$$ , 2007 .
[12] Timothy S. Murphy,et al. Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals , 1993 .
[13] Petra Ostermann,et al. Collocation Methods For Volterra Integral And Related Functional Equations , 2016 .
[14] Daan Huybrechs,et al. On the Evaluation of Highly Oscillatory Integrals by Analytic Continuation , 2006, SIAM J. Numer. Anal..
[15] Jie Shen,et al. Spectral Methods: Algorithms, Analysis and Applications , 2011 .
[16] Shuhuang Xiang,et al. Asymptotic expansion and Filon-type methods for a Volterra integral equation with a highly oscillatory kernel , 2011 .
[17] Shuhuang Xiang,et al. Numerical solutions to Volterra integral equations of the second kind with oscillatory trigonometric kernels , 2013, Appl. Math. Comput..
[18] Shuhuang Xiang,et al. Efficient methods for Volterra integral equations with highly oscillatory Bessel kernels , 2013 .
[19] Kwok Sau Fa,et al. INTEGRO-DIFFERENTIAL EQUATIONS ASSOCIATED WITH CONTINUOUS-TIME RANDOM WALK , 2013 .