Half-explicit Runge-Kutta methods for semi-explicit differential-algebraic equations of index 1.
High order explicit Runge-Kutta pairs for ephemerides of the solar system and the Moon.
Higher-index differential-algebraic equations: analysis and numerical treatment
Highly anisotropic nonlinear temperature balance equation and its numerical solution using asymptotic-preserving schemes of second order in time
This paper deals with the numerical study of a nonlinear, strongly anisotropic heat equation. The use of standard schemes in this situation leads to poor results, due to the high anisotropy. An Asymptotic-Preserving method is introduced in this paper, which is second-order accurate in both, temporal and spacial variables. The discretization in time is done using an L-stable Runge−Kutta scheme. The convergence of the method is shown to be independent of the anisotropy parameter , and this for fixed...