IJPAM: Volume 47, No. 4 (2008)

NUMERICAL INTEGRATORS FOR FOURTH ORDER
INITIAL AND BOUNDARY VALUE PROBLEMS

Samuel N. Jator
Department of Mathematics
Austin Peay State University
Clarksville, TN 37044, USA
e-mail: Jators@apsu.edu


Abstract.In this paper, a continuous $k$-step linear multistep method (LMM) is developed and used to generate new finite difference methods (NFDMs), which are assembled and applied as simultaneous numerical integrators to solve fourth order initial and boundary value problems without reducing them to an equivalent first order system. The NFDMs are analyzed for convergence via consistency and zero-stable by conveniently expressing them as block methods. The initial value problems (IVPs) are solved without the need for either predictors or starting values from other methods, while the boundary value problems (BVPs) are solved by assembling the NFDMs into a single block matrix equation. We illustrate our process using a specific example for $k=4$. Numerical examples are given to show the efficiency of the methods.

Received: August 20, 2008

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

Key Words and Phrases: fourth order, finite difference methods, block methods, multistep methods

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 47
Issue: 4