It is well known that the trapezoidal rule converges geometrically when applied to analytic
functions on periodic intervals or the real line. The mathematics and history of this …

Some of the most effective methods for the numerical inversion of the Laplace transform are
based on the approximation of the Bromwich contour integral. The accuracy of these …

Background The study of dynamic relationship between a multi-species models has gained
a huge amount of scientific interest over the years and will continue to maintain its …

The main target of this monograph is to provide the detailed investigations to the newly
established special functions involving the Mittag-Leffler, Wiman, Prabhakar, Miller–Ross …

Many computational problems can be solved with the aid of contour integrals containing ez
in the integrand: examples include inverse Laplace transforms, special functions, functions …

We consider an initial-boundary value problem for \partial_tu-\partial_t^-α∇^2u=f(t), that is,
for a fractional diffusion (-1<α<0) or wave (0<α<1) equation. A numerical solution is found by …

We study a generalized Crank–Nicolson scheme for the time discretization of a fractional
wave equation, in combination with a space discretization by linear finite elements. The …

We give an algorithm to compute N steps of a convolution quadrature approximation to a
continuous temporal convolution using only O(N\,\logN) multiplications and O(\logN) active …

The fractional diffusion equation is one of the important recent models that can efficiently
characterize various complex diffusion processes, such as in inhomogeneous or …

We consider the discretization in time of a fractional order diffusion equation. The
approximation is based on a further development of the approach of using Laplace …