A class of two-step implicit methods involving higher-order derivatives of y for initial value problems of the form y? = f(t, y, y?)is developed. The methods involve arbitrary parameters p and q, which are determined so that the methods become absolutely stable when applied to the test equation y? + ?y? + ?y = 0. Numerical results for Bessel's and general second-order differential equations are presented to illustrate that the methods are absolutely stable and are of order O(h4), O(h6) and O(h8).

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dc.contributor.authorSesappa Rai, A.
dc.contributor.authorAnanthakrishnaiah, U.
dc.date.accessioned2026-02-05T11:00:33Z
dc.date.issuedObrechkoff methods having additional parameters for general second-order differential equations
dc.description.abstract1997
dc.identifier.citationJournal of Computational and Applied Mathematics, 1997, 79, 2, pp. 167-182
dc.identifier.issn3770427
dc.identifier.urihttps://doi.org/10.1016/S0377-0427(96)00132-X
dc.identifier.urihttps://idr.nitk.ac.in/handle/123456789/28048
dc.publisherElsevier
dc.subjectComputational methods
dc.subjectConvergence of numerical methods
dc.subjectNumerical analysis
dc.subjectProblem solving
dc.subjectInitial value problems
dc.subjectObrechkoff methods
dc.subjectDifferential equations
dc.titleA class of two-step implicit methods involving higher-order derivatives of y for initial value problems of the form y? = f(t, y, y?)is developed. The methods involve arbitrary parameters p and q, which are determined so that the methods become absolutely stable when applied to the test equation y? + ?y? + ?y = 0. Numerical results for Bessel's and general second-order differential equations are presented to illustrate that the methods are absolutely stable and are of order O(h4), O(h6) and O(h8).

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