A family of highly stable second derivative block methods for stiff IVPs in ODEs
R.I. Okuonghae, M.N.O. Ikhile
Department of Mathematics, University of Benin, P.M.B 1154, Benin City, Edo state, Nigeria
Keywords: block methods, continuous methods, collocation and interpolation, boundary locus, A(α)-stability, stiff IVPs
Abstract
This paper considers a class of highly stable block methods for the numerical solution of initial value problems (IVPs) in ordinary differential equations (ODEs). The boundary locus of the proposed parallel one-block, r–output point algorithms shows that the new schemes are A-stable for output points r = 2(2)8 and A(α)-stable for output points r = 10(2)20, where r is the number of processors in a particular block method in the family. Numerical results of the block methods are compared with a second derivative linear multistep method in [8].
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