IJPAM: Volume 50, No. 3 (2009)

BOUNDARY VALUE METHODS VIA A MULTISTEP METHOD
WITH VARIABLE COEFFICIENTS FOR SECOND ORDER
INITIAL AND BOUNDARY VALUE PROBLEMS

S.N. Jator$^1$, J. Li$^2$
$^1$Department of Mathematics
Austin Peay State University
Clarksville, TN 37044, USA
e-mail: [email protected]
$^2$Department of Computer Science and Information Technology
Austin Peay State University
Clarksville, TN 37044, USA


Abstract.Interpolation and collocation procedures are used to construct a linear multistep method (LMM) with variable coefficients from which LMMs with constant coefficients are reproduced. The LMMs are applied as boundary value methods (BVMs) to solve the general second order initial and boundary value problems without first reducing the ordinary differential equation(ODE) into an equivalent first order system. The order, error constant, zero stability and the interval of absolute stability for the LMMs are discussed. We use the specific cases $k=4$ and $k=5$ to illustrate the process. Numerical experiments are performed to show the efficiency of the methods.

Received: January 7, 2009

AMS Subject Classification: 65L05, 65L06, 65L12

Key Words and Phrases: boundary value methods, linear multistep methods, boundary value problem, second order, initial value problem

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 50
Issue: 3