We study the consistency for general additive Runge-Kutta methods in the integration of linear nonhomogeneous problems, obtaining necessary and sufficient conditions of order p, for arbitary values of p. We use this result joined to some A-stability conditions for developing a third order additive Runge-Kutta method of type fractional steps and we show its efficiency in the numerical integration of a two-dimensional evolutionary convection-diffusion problem. © 2002 Elsevier Science B.V. All rights reserved.
Bujanda, B., & Jorge, J. C. (2002). Additive Runge-Kutta methods for the resolution of linear parabolic problems. Journal of Computational and Applied Mathematics, 140(1–2), 99–117. https://doi.org/10.1016/S0377-0427(01)00475-7