A class of A(О±)-stable numerical methods for stiff problems in ordinary differential equations
R.I. Okuonghae
Keywords: stiff IVPs, continuous LMM, collocation and interpolation approach, boundary locus
Abstract
The A(α)-stable numerical methods (ANM) for the number of steps k ≤ 7 for stiff initial value problems (IVPs) in ordinary differential equations (ODEs) are proposed. The discrete schemes proposed from their equivalent continuous schemes are obtained. The scaled time variable t in a continuous method, which determines the discrete coefficients of the discrete method is chosen in such a way as to ensure that the discrete scheme attains a high order and A(α)-stability. We select the value of α for which the schemes proposed are absolutely stable. The new algorithms are found to have a comparable accuracy with that of the backward differentiation formula (BDF) discussed in [12] which implements the Ode15s in the Matlab suite.
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