1. Journal Articles
Permanent URI for this collectionhttps://idr.nitk.ac.in/handle/1/6
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Item Obrechkoff methods having additional parameters for general second-order differential equations(1997) Sesappa, Rai, A.; Ananthakrishnaiah, U.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).Item Additive parameters methods for the numerical integration of y? = f (t, y, y?)(1996) Sesappa, Rai, A.; Ananthakrishnaiah, U.In this paper numerical methods for the initial value problems of general second order differential equations are derived. The methods depend upon the parameters p and q which are the new additional values of the coefficients of y? and y in the given differential equation. Here, we report a new two step fourth order method. As p tends to zero and q ? (2?/h)2 the method is absolutely stable. Numerical results are presented for Bessel's, Legendre's and general second order differential equations.Item A class of two-step P-stable methods for the accurate integration of second order periodic initial value problems(1986) Ananthakrishnaiah, U.In this paper we consider a two parameter family of two-step methods for the accurate numerical integration of second order periodic initial value problems. By applying the methods to the test equation y? + ?2y = 0, we determine the parameters ?, ? so that the phase-lag (frequency distortion) of the method is minimal. The resulting method is a P-stable method with a minimal phase-lag ?6h6/42000. The superiority of the method over the other P-stable methods is illustrated by a comparative study of the phase-lag errors and by illustrating with a numerical example. 1986.