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Okuonghae, R. I.; Ikhile, M. N. O.

The numerical solution of stiff IVPs in ODEs using modified second derivative BDF. (English) Zbl 1273.65099

Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 51, No. 1, 51-77 (2012).
Summary: This paper considers modified second derivative backward differentiation formulas (BDF) for the numerical solution of stiff initial value problems (IVPs) in ordinary differential equations (ODEs). The methods are A\((\alpha)\)-stable for the step length \(k\leq 7\).

Cited in 1 Document

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L04 Numerical methods for stiff equations
34A34 Nonlinear ordinary differential equations and systems
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations

Keywords:

second derivative BDF; collocation; interpolation; initial value problem; stiff stability; boundary locus; numerical examples; multistep method; backward differentiation formulas (BDF)

Software:

RODAS
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\textit{R. I. Okuonghae} and \textit{M. N. O. Ikhile}, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 51, No. 1, 51--77 (2012; Zbl 1273.65099)
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References:

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