IJPAM: Volume 21, No. 1 (2005)

NUMEROV-TYPE P-STABLE LINEARLY
IMPLICIT SCHEMES FOR SECOND ORDER
INITIAL VALUE PROBLEMS

M.M. Chawla
Department of Mathematics and Computer Science
Kuwait University
P.O. Box 5969, Safat, 13060, KUWAIT
e-mail: chawla@mcs.sci.kuniv.edu.kw


Abstract.For the integration of special second order initial value problems with oscillatory solutions, P-stable schemes are necessarily implicit. For nonlinear problems, functional implicitness of these schemes requires the use of Newton's method at each time-step of integration. In the present paper, we propose linearized linearly implicit P-stable schemes which, for nonlinear problems, obviate the need to solve resulting nonlinear equations. We present two such schemes. First, we present a second order scheme and then a fourth order linearly implicit P-stable Numerov-type scheme. The obtained schemes are computationally illustrated for their order, accuracy and stability by considering two examples of practical interest.

Received: March 17, 2005

AMS Subject Classification: 65L05

Key Words and Phrases: second order initial value problems, oscillatory solutions, P-stability, linearly implicit schemes, second order method, Numerov-type method

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 21
Issue: 1