Boundary Locus Search for Stiffly Stable Second Derivative Linear Multistep Formulas for Stiff ODEs


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A? Stability, Stiffly stable, Initial value problem (ivp), Ordinary differential equation (ode)


High order numerical schemes are mostly desired for the integration of stiff initial value problems. In this paper, stable second
derivative linear multistep formulas of high order of accuracy are derived by the inclusion of a nonzero coefficient selected out
of k zero coefficients of the third characteristics polynomial of conventional second derivative backward differentiation
formulas. One coefficient out of k zero coefficients is assumed nonzero one at a time and this results in the development of
k new second derivative linear multistep formulas. Boundary locus technique is thereafter used to analyze the stability of these
new k second derivative linear multistep formulas. Stable members of these formulas are shown to be
A? stable for order p ? 4 and A(?)-stable for order p ?11 . Numerical examples are included to justify the suitability of these schemes as numerical integrators for stiff initial value problem

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