The family of three-level fifth-order time integrators are considered for hyperbolic, parabolic PDEs and stiff ODEs. They are classified into two parts depending on positivity or negativity of the operators corresponding to the second time derivatives. Two options are presented for hyperbolic equations. Stability analysis is performed for linear cases. It is shown that the scheme for ODEs can be nearly A-stable and nearlyL -stable for particular values of its free parameter. Numerical illustration is presented for hyperbolic case.
Positivity – Springer Journals
Published: Oct 7, 2004
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