In this paper we study a class of integrodifferential equations considered in an arbitrary Banach space. Using the theory of analytic semigroups we establish the existence, uniqueness, regularity and continuation of solutions to these integrodifferential equations.

: : In this paper, we present a new approach to resolve linear weakly-singular partial integro-differential equations by first removing the singularity using Taylor's approximation and transform the given partial integrodifferential equations into an partial differential equation. After that the fourth order compact finite difference scheme and collocation method is presented to obtain system o...

In the present paper, we provide an analytical expression for the first- and second-order velocity slip coefficients by means of a variational technique that applies to the integrodifferential form of the Boltzmann equation based on the true linearized collision operator and the Cercignani-Lampis scattering kernel of the gas-surface interaction. The polynomial form of the Knudsen number obtaine...

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 memory. The method does not require evaluations of the convolution kernel, but instead O(logN) evaluations of its Laplace transform, which is assumed sectorial. The algorithm can be used for the stable numerical solution w...