SERK2
swMATH ID:  10426 
Software Authors:  Kleefeld, B.; MartínVaquero, J. 
Description:  SERK2v2: A new secondorder stabilized explicit RungeKutta 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 RungeKutta methods (also called RungeKuttaChebyshev methods) were proposed to try to avoid these difficulties. The RungeKutta 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. MartínVaquero 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 sixthorder polynomials. Here, we develop a new method based on secondorder 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 wellknown secondorder methods such as RKC and ROCK2. 
Homepage:  http://onlinelibrary.wiley.com/doi/10.1002/num.21704/abstract 
Related Software:  SERK2v3; RKC; RODAS; MEBDF; SROCK; 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 secondorder stabilized explicit RungeKutta method for stiff problems. Zbl 1258.65066 Kleefeld, B.; MartínVaquero, J. 
2013

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Cited by 20 Authors
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Cited in 6 Serials
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