SERK2 swMATH ID: 10426 Software Authors: Kleefeld, B.; Martín-Vaquero, J. Description: SERK2v2: A new second-order stabilized explicit Runge-Kutta method for stiff problems. Traditionally, explicit numerical algorithms have not been used with stiff ordinary differential equations (ODEs) due to their stability. Implicit schemes are usually very expensive when used to solve systems of ODEs with very large dimension. Stabilized Runge-Kutta methods (also called Runge-Kutta-Chebyshev methods) were proposed to try to avoid these difficulties. The Runge-Kutta methods are explicit methods with extended stability domains, usually along the negative real axis. They can easily be applied to large problem classes with low memory demand, they do not require algebra routines or the solution of large and complicated systems of nonlinear equations, and they are especially suited for discretizations using the method of lines of two and three dimensional parabolic partial differential equations. In J. Martín-Vaquero and B. Janssen [ Comput. Phys. Commun. 180, No. 10, 1802–1810 (2009; bl 1197.65006)], we showed that previous codes based on stabilized Runge–Kutta algorithms have some difficulties in solving problems with very large eigenvalues and we derived a new code, SERK2, based on sixth-order polynomials. Here, we develop a new method based on second-order polynomials with up to 250 stages and good stability properties. These methods are efficient numerical integrators of very stiff ODEs. Numerical experiments with both smooth and nonsmooth data support the efficiency and accuracy of the new algorithms when compared to other well-known second-order methods such as RKC and ROCK2. Homepage: http://onlinelibrary.wiley.com/doi/10.1002/num.21704/abstract Related Software: SERK2v3; RKC; RODAS; MEBDF; S-ROCK; DASSL; VODE; IRKC; Mathematica; M3RK Cited in: 12 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year SERK2v2: A new second-order stabilized explicit Runge-Kutta method for stiff problems. Zbl 1258.65066Kleefeld, B.; Martín-Vaquero, J. 2013 all top 5 Cited by 20 Authors 7 Martín-Vaquero, Jesús 4 Kleefeld, B. 3 Kleefeld, Andreas 2 Khaliq, Abdul Q. M. 2 Wade, Bruce A. 1 Asante-Asamani, E. O. 1 Bhatt, Harish P. 1 Encinas, A. H. 1 Fellouah, Hachimi 1 Hernández Guillén, J. D. 1 Hoang, Thi-Thao-Phuong 1 Ju, Lili 1 Kessal, Mohand 1 Li, Xiao 1 Martín del Rey, Ángel 1 Mouloud, A. 1 Queiruga-Dios, Araceli 1 Rodríguez Sánchez, Gerardo 1 Tang, Xiao 1 Xiao, Aiguo all top 5 Cited in 6 Serials 5 Journal of Computational and Applied Mathematics 3 Journal of Computational Physics 1 Computers & Mathematics with Applications 1 BIT 1 Mathematics and Computers in Simulation 1 Numerical Methods for Partial Differential Equations all top 5 Cited in 6 Fields 12 Numerical analysis (65-XX) 6 Partial differential equations (35-XX) 1 Probability theory and stochastic processes (60-XX) 1 Fluid mechanics (76-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX) Citations by Year