Document Type
Article
Rights
This item is available under a Creative Commons License for non-commercial use only
Disciplines
1.1 MATHEMATICS
Abstract
Abstract. Explicit numerical methods for the solution of a system of stiff differential equations suffer from a time step size that approaches zero in order to satisfy stability conditions. Implicit schemes allow a larger time-step, but require more computations. When the differential equations are dominated by a skew-symmetric component, the problem is not stiffness in the sense that the size of the eigenvalues are unequal, rather the that the real eigenvalues are dominated by imaginary eigenvalues. We present and compare analytical results for stable time step limits for several explicit methods including the super-time-stepping method of Alexiades, Amiez, and Gremaud which is a explicit Runge-Kutta method for parabolic partial differential equations and a new method modeled on a predictor-corrector scheme with multiplicative operator splitting. This new explicit method, presented in regular and super-time-stepping form, increases stability without forcing the step size to zero.
DOI
http://doi.org10.1137/090775804
Recommended Citation
Gurski, K., O'Suillivan, S. (2011) A stability study of a new explicit numerical scheme for a system of differential equations with a large skew-symmetric component, SIAM Journal on Numerical Analysis, 49 (1), 368-386 doi:10.1137/090775804 doi/abs/10.1137/090775804
Publication Details
SIAM Journal on Numerical Analysis, 2011, 49 (1), 368-386
doi/abs/10.1137/090775804