Time discretization of an evolution equation via Laplace transforms

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Numerical solution via Laplace transforms of a fractional order evolution equation (2010, methodology): “The methods are combined with finite element discretization in the spatial variables to yield fully discrete methods.”
The Exponentially Convergent Trapezoidal Rule (2014, unknown): “Relevant papers include [56, 81, 180, 181] (parabolic contours), [105, 121, 148, 181] (hyperbolic contours), and [38, 171] (Talbot contours).”
Talbot quadratures and rational approximations (2006, methodology): “... methods generalize in natural ways to large-scale problems involving fine discretizations and large matrices, where they are readily utilized in the context of Krylov subspace iterations and multiple processors [7, 8]. And they are readily generalized to problems with singularities off R−, inclu”
Maximum-norm error analysis of a numerical solution via Laplace transformation and quadrature of a fractional-order evolution equation (2010, methodology): “We begin with a nonsmooth data error estimate for the semidiscrete problem, which was shown in (McLean and Thomée, 2004, Theorem 5.1) for 0 α 1.”