Third order two-step Runge–Kutta–Chebyshev methods

Abstract

The well-known high order stabilized codes (such as DUMKA and ROCK) have several drawbacks: numerically obtained stability polynomials (which do not have a closed analytic form), poor internal stability and convergence. RKC-type methods have much better computational properties. However, these types of methods currently have a second order maximum. In this paper, a family of third order stabilized methods with an explicit analytical solution of stability polynomials is presented. This was made possible by usage of two-step Runge–Kutta methods. A new code TSRKC3 is proposed, illustrated by several examples, and compared to existing programs.