Applied Numerical Mathematics 

TL;DR: Runge-Kutta-based IMEX schemes are developed that have better stability regions than the best known IMEX multistep schemes over a wide parameter range.

TL;DR: In this paper, a fully discrete difference scheme is derived for a diffusion-wave system by introducing two new variables to transform the original equation into a low order system of equations. And the solvability, stability and L∞ convergence are proved by the energy method.

TL;DR: This paper describes an implementation of a parallel AMG code, using the algorithm of A.J. Cleary, and considers three basic coarsening schemes and certain modifications to the basic schemes, designed to address specific performance issues.

TL;DR: In this paper, the authors examined some practical numerical methods to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain, and the stability, consistency, and (therefore) convergence of the methods are discussed.

TL;DR: Additive Runge-Kutta (ARK) methods are investigated for application to the spatially discretized one-dimensional convection-diffusion-reaction (CDR) equations and results for the fifth-order method are disappointing, but both the new third- and fourth-order methods are at least as efficient as existing ARK2 methods.