Browsing by Author "Krishnaiah, U.A."

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Adaptive methods for periodic initial value problems of second order differential equations
(1982) Krishnaiah, U.A.
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.
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.
1981
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
Inverse linear multistep methods for the numerical solution of initial value problems of second order differential equations
(1981) Krishnaiah, U.A.
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.