Browsing by Author "Saldanha, G."

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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.
(A fourth?order finite difference scheme for two?dimensional nonlinear elliptic partial differential equations) Saldanha, G.; Ananthakrishnaiah, U.
1995
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.
Symmetric multistep methods with zero phase-lag for periodic initial value problems of second order differential equations
(2006) Saldanha, G.; Achar, S.D.
We present in this paper two-step and four-step symmetric multistep methods involving a parameter p to solve a special class of initial value problems associated with second order ordinary differential equations in which the first derivative does not appear explicitly. It is shown that the methods have zero phase-lag when p is chosen as 2? times the frequency of the given initial value problem. The periodicity intervals are given in terms of expressions involving the parameter p. As p increases, the periodicity intervals increase and for large p, the methods are almost P-stable. 2005 Elsevier Inc. All rights reserved.
Symmetric multistep methods with zero phase-lag for periodic initial value problems of second order differential equations
(2006) Saldanha, G.; Achar, S.D.
We present in this paper two-step and four-step symmetric multistep methods involving a parameter p to solve a special class of initial value problems associated with second order ordinary differential equations in which the first derivative does not appear explicitly. It is shown that the methods have zero phase-lag when p is chosen as 2? times the frequency of the given initial value problem. The periodicity intervals are given in terms of expressions involving the parameter p. As p increases, the periodicity intervals increase and for large p, the methods are almost P-stable. © 2005 Elsevier Inc. All rights reserved.