Rai, Sesappa A and Ananthakrishnaiah, U (1997) Obrechkoff methods having additional parameters for general second-order differential equations. Journal of Computational and Applied Mathematics, 27 (2). pp. 167-182. ISSN 0377-0427

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Abstract

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" + 2y' + #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(h 6) and O(hS).

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