Solving A x = b Using a Modified Conjugate Gradient Method Based on Roots of A
نویسندگان
چکیده
In this paper we review and further develop a class of strong stability-preserving (SSP)high-order time discretizations for semidiscrete method of lines approximations of par-tial differential equations. Previously termed TVD (total variation diminishing) timediscretizations, these high-order time discretization methods preserve the strong stabil-ity properties of first-order Euler time stepping and have proved very useful, especiallyin solving hyperbolic partial differential equations. The new developments in this paperinclude the construction of optimal explicit SSP linear Runge–Kutta methods, their appli-cation to the strong stability of coercive approximations, a systematic study of explicit SSPmultistep methods for nonlinear problems, and the study of the SSP property of implicitRunge–Kutta and multistep methods.
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