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Item In this paper inverse linear multistep methods for the numerical solution of second order differential equations are presented. Local accuracy and stability of the methods are defined and discussed. The methods are applicable to a class of special second order initial value problems, not explicitly involving the first derivative. The methods are not convergent, but yield good numerical results if applied to problems they are designed for. Numerical results are presented for both the linear and nonlinear initial value problems. © 1981.(Inverse linear multistep methods for the numerical solution of initial value problems of second order differential equations) Krishnaiah, U.A.1981Item A new generalized algorithm, which can be programmed on a digital computer, is established for performing the inversion of the Cauer type continued fractions. © 1980 IEEE(A Generalized Algorithm for the Inversion of Cauer Type Continued Fractions) Parthasarathy, R.; John, S.1980Item 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.(A class of two-step P-stable methods for the accurate integration of second order periodic initial value problems) Ananthakrishnaiah, U.1986Item In this paper E-stable methods of O(h4), O(h8) and O(h12) are derived for the direct numerical integration of initial value problems of second order differential equations with exponentially decreasing solutions. Numerical results are presented for both linear and nonlinear problems. © 1985 BIT Foundations.(Kluwer Academic Publishers, E-stable methods for exponentially decreasing solutions of second order initial value problems) Ananthakrishnaiah, U.1985Item In this paper numerical methods involving higher order derivatives for the solution of periodic initial value problems of second order differential equations are derived. The methods depend upon a parameter p > 0 and reduce to their classical counter parts as p ? 0. The methods are periodically stable when the parameter p is chosen as the square of the frequency of the linear homogeneous equation. The numerical methods involving derivatives of order up to 2q are of polynomial order 2q and trigonometric order one. Numerical results are presented for both the linear and nonlinear problems. The applicability of implicit adaptive methods to linear systems is illustrated. © 1982.(Adaptive methods for periodic initial value problems of second order differential equations) Krishnaiah, U.A.1982