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 E-stable methods for exponentially decreasing solutions of second order initial value problems(1985) Ananthakrishnaiah, U.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.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 fourth?order finite difference scheme for two?dimensional nonlinear elliptic partial differential equations(1995) Saldanha, G.; Ananthakrishnaiah, U.A finite difference scheme for the two?dimensional, second?order, nonlinear elliptic equation is developed. The difference scheme is derived using the local solution of the differential equation. A 13?point stencil on a uniform mesh of size h is used to derive the finite difference scheme, which has a truncation error of order h4. Well?known iterative methods can be employed to solve the resulting system of equations. Numerical results are presented to demonstrate the fourth?order convergence of the scheme. 1995 John Wiley & Sons, Inc. Copyright 1995 Wiley Periodicals, Inc.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.