From c53d62e9a582750c4ebdfdfe5b8b1b1810f29d5c Mon Sep 17 00:00:00 2001 From: Hendrik Ranocha Date: Sun, 12 Jul 2020 11:53:17 +0200 Subject: [PATCH] minor revisions --- paper.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/paper.md b/paper.md index fe70b69..486939e 100644 --- a/paper.md +++ b/paper.md @@ -82,8 +82,8 @@ it has been used in a number of papers (see below). This package computes optimal stability functions for Runge-Kutta methods. Here optimal means that the stable step size is maximized for a given ODE spectrum. The corresponding optimization problem is intractable under a -direct implementation. The package uses the algorithm developed in -[@2012_optimal_stability_polynomials], which transforms the problem into a +direct implementation. The package uses the algorithm developed by +@2012_optimal_stability_polynomials, which transforms the problem into a sequence of convex problems and typically yields a solution in a few seconds or less. This package is usually used as the first step in designing a Runge-Kutta method. @@ -116,8 +116,8 @@ involving downwind Runge-Kutta methods and low-storage Runge-Kutta methods. ## `am_radius-opt` Whereas the previous two subpackages are fairly general-purpose tools, -this package solves a very specific set of problems described in -[@2009_monotonicity]. Specifically, the provided routines determine the cofficients of +this package solves a very specific set of problems described by +@2009_monotonicity. Specifically, the provided routines determine the coefficients of multistep methods (including classes of general linear methods) with the largest possible SSP coefficient (also known as radius of absolute monotonicity). The corresponding optimization problem