Faculty Publications
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Item 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.(Elsevier, Additive parameters methods for the numerical integration of y? = f (t, y, y?)) Sesappa Rai, A.; Ananthakrishnaiah, U.1996Item 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).(Elsevier, Obrechkoff methods having additional parameters for general second-order differential equations) Sesappa Rai, A.; Ananthakrishnaiah, U.1997