Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 25, Issue 1, Pages 105-128Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-004-4635-5
Keywords
strong stability preserving; Runge-Kutta methods; multi step methods; high order accuracy; time discretization
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Strong stability preserving (SSP) high order time discretizations were developed for solution of semi-discrete method of lines approximations of hyperbolic partial differential equations. These high order time discretization methods preserve the strong stability properties-in any norm or seminorm-of the spatial discretization coupled with first order Euler time stepping. This paper describes the development of SSP methods and the recently developed theory which connects the timestep restriction on SSP methods with the theory of monotonicity and contractivity. Optimal explicit SSP Runge-Kutta methods for nonlinear problems and for linear problems as well as implicit Runge-Kutta methods and multi step methods will be collected.
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